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Method using forcing to construct sets with desired properties in computability theory
Forcing in computability theory is a modification of Paul Cohen's original set-theoretic technique of forcing to deal with computability concerns. Conceptually
Forcing_(computability)
Study of computable functions and Turing degrees
these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include:
Computability_theory
Technique invented by Paul Cohen for proving consistency and independence results
logic such as computability theory. Descriptive set theory uses the notions of forcing from both computability theory and set theory. Forcing has also been
Forcing_(mathematics)
Topics referred to by the same term
independence proofs for set theory Forcing (computability), a modification of Paul Cohen's original set theoretic technique of forcing to deal with the effective
Forcing
Problem-solving technique and algorithmic paradigm
Practitioners. Springer. p. 7. ISBN 978-3-642-04100-6. A brute-force algorithm to solve Sudoku puzzles. Brute-force attack Big O notation Iteration#Computing
Brute-force_search
Overview of and topical guide to logic
thesis Computability logic Computable function Computation Decision problem Effective method Entscheidungsproblem Enumeration Forcing (computability) Halting
Outline_of_logic
Subfield of mathematics
adopted throughout mathematics. The study of computability came to be known as recursion theory or computability theory, because early formalizations by Gödel
Mathematical_logic
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
Thesis on the nature of computability
In computability theory, the Church–Turing thesis is a thesis about the nature of computable functions. It states that a function on the natural numbers
Church–Turing_thesis
{\displaystyle \Pi _{1}^{0}} classes in computability theory". In Griffor, Edward R. (ed.). Handbook of computability theory. Stud. Logic Found. Math. Vol
Low_basis_theorem
Computation model defining an abstract machine
each producing output data from given input data. Computability theory, which studies computability of functions from inputs to outputs, and for which
Turing_machine
Form of shared internet-based computing
Cloud computing is defined by the International Organization for Standardization (ISO) as "a paradigm for enabling network access to a scalable and elastic
Cloud_computing
Computer hardware technology that uses quantum mechanics
computers provide no additional power over classical computers in terms of computability. This means that quantum computers cannot solve undecidable problems
Quantum_computing
Set with algorithmic membership test
In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every
Computable_set
examplesPages displaying short descriptions of redirect targets in computability Rasiowa–Sikorski lemma – Mathematical lemma K. Ciesielski (1997). Set
Generic_filter
American mathematician
theory (particularly the idea of the set-theoretic multiverse), in computability theory, and in group theory. After earning a Bachelor of Science in
Joel_David_Hamkins
syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms. Peano axioms Giuseppe
List of mathematical logic topics
List_of_mathematical_logic_topics
presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church's
Timeline of mathematical logic
Timeline_of_mathematical_logic
A forcing, and Shelah, who introduced proper forcing. Revised countable support iteration was introduced by Shelah to handle semi-proper forcings, such
List_of_forcing_notions
American mathematician
has done other work in mathematical logic, primarily in the area of computability theory. His doctoral students at the University of Chicago have included
Robert_I._Soare
Series of GPUs by Nvidia
hardware-accelerated real-time ray tracing and fifth-generation Tensor Cores for AI compute and performing floating-point calculations. RTX 50 series GPUs are the
GeForce_RTX_50_series
Series of GPUs by Nvidia
Asynchronous compute on Maxwell therefore requires that both a game and the GPU driver be specifically coded for asynchronous compute on Maxwell in order
GeForce_900_series
Yes/no problem in computer science
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a
Decision_problem
Parallel computing platform and programming model
CUDA (Compute Unified Device Architecture) is a proprietary parallel computing platform and application programming interface (API) developed by the American
CUDA
Mathematical logic concept
In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable
Computably_enumerable_set
Programmable machine that processes data
organizations, clubs and societies of both a formal and informal nature. Computability theory Computer security Glossary of computer hardware terms History
Computer
Distributed computing paradigm
Furthermore, devices at the edge constantly consume data coming from the cloud, forcing companies to decentralize data storage and service provisioning, leveraging
Edge_computing
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
Yes-or-no question that cannot ever be solved by a computer
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct
Undecidable_problem
Series of GPUs by Nvidia
2013. Retrieved December 11, 2015. "Nvidia's GeForce GTX Titan, Part 1: Titan For Gaming, Titan For Compute". Anandtech.com. Archived from the original on
GeForce_700_series
Open internet standards organization
The Internet Engineering Task Force (IETF) is a standards organization for the Internet responsible for the technical standards of the Internet protocol
Internet Engineering Task Force
Internet_Engineering_Task_Force
US customary unit of force
e. one half of a short ton). Another use is as a unit of deadweight to compute shipping charges. 1 kip ≈ 4,448.222 N = 4.448222 kN The name comes from
Kip_(unit)
Feedback between climate change and the effect of clouds on radiation
referred to as cloud radiative forcing (CRF). However, since cloud changes are not normally considered an external forcing of climate, CRE is the most commonly
Cloud_feedback
Series of GPUs by Nvidia
released the GeForce RTX 3090 Ti on March 29, 2022. Architectural improvements of the Ampere architecture include the following: CUDA Compute Capability 8
GeForce_RTX_30_series
American multinational technology company
online advertising, search engine technology, email, cloud computing, software, quantum computing, e-commerce, consumer electronics, and artificial intelligence
Mathematical transformation
mechanical force exerted on a piston. Compute the force on the plates as a function of x, the distance which separates them. To find the force, compute the potential
Legendre_transformation
events in the history of computing from 1950 to 1979. For narratives explaining the overall developments, see the history of computing. Information revolution
Timeline of computing 1950–1979
Timeline_of_computing_1950–1979
Whether a decision problem has an effective method to derive the answer
This is closely related to the concept of a many-one reduction in computability theory. A property of a theory or logical system weaker than decidability
Decidability_(logic)
GPU microarchitecture designed by Nvidia
GB203 which was not the case with AD102 over AD103. CUDA Compute Capability 10.0 and Compute Capability 12.0 are added with Blackwell. The Blackwell architecture
Blackwell_(microarchitecture)
Series of GPUs by Nvidia
Samsung's newer 14 nm process (GP107, GP108). New Features in GP10x: CUDA Compute Capability 6.0 (GP100 only), 6.1 (GP102, GP104, GP106, GP107, GP108) DisplayPort
GeForce_10_series
Series of GPUs by Nvidia
highlights of the Ada Lovelace architecture include the following: CUDA Compute Capability 8.9 TSMC 4N process (5 nm custom designed for Nvidia) – not
GeForce_RTX_40_series
Influence that can change motion of an object
In physics, a force is an action that can cause an object to change its velocity or its shape, or to resist other forces, or to cause changes of pressure
Force
Date and time from which a computer measures system time
In computing, an epoch is a fixed date and time used as a reference from which a computer measures system time. Most computer systems determine time as
Epoch_(computing)
American multinational technology company
company's product lines include GeForce GPUs for gaming and creative workloads, and professional GPUs for edge computing, scientific research, and industrial
Nvidia
English mathematician (1815–1852)
Computability". Ada Lovelace Day. FindingAda.com. 31 January 2016. Retrieved 11 January 2016. "The Ada Lovelace Bicentenary Lectures on Computability"
Ada_Lovelace
Nizam of Hyderabad from 1751 to 1762
1752 his force computed to amount to 150,000 men. When intelligence of his arrival reached Hyderabad, Salabat Jung, marched out with a great force to oppose
Salabat_Jung
Trauma to the body without penetration of the skin
A blunt trauma, also known as a blunt force trauma or non-penetrating trauma, is a physical trauma due to a forceful impact without penetration of the
Blunt_trauma
removing a character from play, deleting progress, resetting a world, or forcing the player to begin again. Because permadeath reduces the reversibility
Death_in_video_games
The history of computing extends beyond the history of computing hardware and modern computing technology including earlier methods that relied on pen
History_of_computing
Programming paradigm in which many processes are executed simultaneously
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided
Parallel_computing
American businessman (born 1964)
president and CEO of Amazon, the world's largest e-commerce and cloud computing company. According to the Bloomberg Billionaires Index and Forbes, he
Jeff_Bezos
Series of GPUs by Nvidia
units GeForce GTX 295 die (GT200-350-B3) Compute Capability: 1.1 (G92 [GTS250] GPU) Compute Capability: 1.2 (GT215, GT216, GT218 GPUs) Compute Capability:
GeForce_200_series
computing from 2020 to the present. For narratives explaining the overall developments, see the history of computing. Significant events in computing
Timeline of computing 2020–present
Timeline_of_computing_2020–present
Branch of computational complexity theory
inputs. All other inputs are free for use. Therefore, one simply brute-force compute all 2 2 d {\displaystyle 2^{2^{d}}} possible inputs. If a certain input
Parameterized_complexity
Topics referred to by the same term
systems Internal security, the work of keeping domestic peace by a national force International studies, or International relations, the study of politics
IS
GPU microarchitecture by Nvidia
Ampere architecture include the following: CUDA Compute Capability 8.0 for A100 and 8.6 for the GeForce 30 series TSMC's 7 nm FinFET process for A100 Custom
Ampere_(microarchitecture)
Measure of computer performance
(FLOPS, flops or flop/s) is a measure of computer performance or compute in computing, useful in fields of scientific computations that require floating-point
Floating point operations per second
Floating_point_operations_per_second
Placeholder variables in programming
all recognition). According to an RFC from the Internet Engineering Task Force, the word FOO originated as a nonsense word with its earliest documented
Foobar
Series of GPUs by Nvidia
The GeForce GTX 16 series is a series of graphics processing units (GPUs) developed by Nvidia, based on the Turing microarchitecture, announced in February
GeForce_GTX_16_series
Series of GPUs by Nvidia
G200 series to be compute capability 1.3, while Fermi-based cards have compute capability 2.x (page 14, Section 2.5). NVIDIA Fermi Compute Architecture Whitepaper
GeForce_400_series
Data item stored in a browser by a website
unchanged, used by Unix programmers. Magic cookies were already used in computing when computer programmer Lou Montulli had the idea of using them in web
HTTP_cookie
Brand of GPUs by Nvidia
general-purpose graphics processor unit (GPGPU) market thanks to their proprietary Compute Unified Device Architecture (CUDA). GPGPU is expected to expand GPU functionality
GeForce
Set of all true first-order statements about the arithmetic of natural numbers
184 Boolos, George; Burgess, John P.; Jeffrey, Richard C. (2002), Computability and logic (4th ed.), Cambridge University Press, ISBN 978-0-521-00758-0
True_arithmetic
except the GeForce 205, 210, 220, & GT 240, which support Direct3D 10.1 instead. Compute Capability: 1.1 (G92 [GTS250] GPU). Compute Capability: 1.2
List of Nvidia graphics processing units
List_of_Nvidia_graphics_processing_units
events in the history of computing from 2000 to 2009. For narratives explaining the overall developments, see the history of computing. Information Age "Windows
Timeline of computing 2000–2009
Timeline_of_computing_2000–2009
Method of solving computing problems
Ultimate Computing. Elsevier Science Publishers. ISBN 978-0-444-70283-8. R.L. Epstein and W.A. Carnielli (1989); Computability, Computable Functions
Lateral_computing
Molecular simulation technique
(2009). "Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-field-based electrostatics"
Reaction_field_method
Initiative to rethink the concept of computing
The Task Force on Rebooting Computing (TFRC), housed within IEEE Computer Society, is the new home for the IEEE Rebooting Computing Initiative. Founded
IEEE_Rebooting_Computing
Supercomputer platform
affordable high-performance computing. PlayStation 3 clusters have had different configurations. A distributed computing system utilizing PlayStation
PlayStation_3_cluster
Software development company
Bright Computing, Inc. was a developer of software for deploying and managing high-performance (HPC) clusters, Kubernetes clusters, and OpenStack private
Bright_Computing
Medical imaging procedure
A computed tomography scan (CT scan), formerly known in a more rudimentary state as computed axial tomography scan (CAT scan), is a medical imaging technique
CT_scan
Device that forwards data packets between computer networks
University of California, Santa Barbara, and the University of Utah School of Computing in the United States. All were built with the Honeywell 516. These computers
Router_(computing)
Measure of supercomputer performance
Zettascale computing refers to computing systems capable of calculating at least "1021 IEEE 754 Double Precision (64-bit) operations (multiplications
Zettascale_computing
American logician (1943–2011)
filters, ideals, and partition relations, iterated forcing and Axiom A, proper forcing and the proper forcing axiom, chromatic number of graphs, a thin very-tall
James_Earl_Baumgartner
Development platform for rendering graphics
Nvidia RTX (also known as Nvidia GeForce RTX under the GeForce brand) is a professional visual computing platform created by Nvidia, used in mainstream
Nvidia_RTX
2014 book by Denis Hirschfeldt
also review some of the tools needed in this study, including computability theory, forcing, and the low basis theorem. Chapter six, "the real heart of
Slicing_the_Truth
Brand by Nvidia
GeForce Now (stylized as GeForce NOW) is the brand used by Nvidia for its cloud gaming service. Nvidia Grid, Nvidia's cloud gaming service for Nvidia Shield
GeForce_Now
Field of study to extract knowledge from data
an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processing, scientific visualization, algorithms
Data_science
1994 multi-role combat aircraft family by Eurofighter
a speech recognition module (SRM), developed by Smiths Aerospace and Computing Devices. It was the first production DVI system used in a military cockpit
Eurofighter_Typhoon
Paradigm of outsourcing
(managed services providers) increasingly facing the challenge of cloud computing, a number of MSPs are providing in-house cloud services or acting as brokers
Managed_services
GPU microarchitecture by Nvidia
improvements of the Ada Lovelace architecture include the following: CUDA Compute Capability 8.9 TSMC 4N process (custom designed for Nvidia) - not to be
Ada Lovelace (microarchitecture)
Ada_Lovelace_(microarchitecture)
Semiconductor memory supply crisis
limited supply of AI chips has been cited as a reason for the slow down in compute growth. In October 2025, OpenAI formally announced a strategic partnership
2025–present global memory supply shortage
2025–present_global_memory_supply_shortage
Series of GPUs by Nvidia
Compute Capability: 1.1 has support for Atomic functions, which are used to write thread-safe programs. All graphical processing units in the GeForce
GeForce_9_series
Dimensionless quantity in fluid dynamics
using pressure differential to compute Mach number, not temperature. Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible
Mach_number
Force tending to bend a structural element
implicit assumptions. The descriptions below use vector mechanics to compute moments of force and bending moments in an attempt to explain, from first principles
Bending_moment
GPU by Nvidia
GeForce 256 is the original release in Nvidia's "GeForce" product line. Announced on August 31, 1999 and released on October 11, 1999, the GeForce 256
GeForce_256
Cryptanalytic method for unauthorized users to access data
Brute-force Attack". ZDNet. Archived from the original on June 26, 2010. Landauer, L (1961). "Irreversibility and Heat Generation in the Computing Process"
Brute-force_attack
Part of the Vietnam War (1968–1972)
times during the same time period. The Air Force's computing of communist personnel losses, according to Air Force historian Bernard Nalty was "based on so
Operation_Commando_Hunt
Messaging and VoIP service owned by Meta
application for all members of group chat, which could only be fixed by forcing the complete uninstall and reinstall of the app. The bug was discovered
Software infrastructure system
Retrieved 8 February 2016. Patrick Hubbard. "Hyper-converged infrastructure forcing new thinking for networks". Techtarget. Archived from the original on 29
Hyper-converged infrastructure
Hyper-converged_infrastructure
Web browser developed by Google
Chrome's design bridges the gap between desktop and so-called "cloud computing". At the touch of a button, Chrome lets you make a desktop, Start menu
Google_Chrome
American multinational technology company
U.S. patents generated by a business. IBM was founded in 1911 as the Computing-Tabulating-Recording Company (CTR), a holding company of manufacturers
IBM
Topics referred to by the same term
(periodic table), a column in the periodic table of chemical elements Group (computing), a collection of users or other objects Group (database) Group (online
Group
Branch of mathematics that studies sets
of forcing while searching for a model of ZFC in which the continuum hypothesis fails, or a model of ZF in which the axiom of choice fails. Forcing adjoins
Set_theory
Computer communications authentication algorithm
the hash function (e.g. 64 bytes for SHA-1) // Compute the block sized key block_sized_key = computeBlockSizedKey(key, hash, blockSize) o_key_pad ← block_sized_key
HMAC
Racing steering wheel from Logitech
2021. "Logitech G29 Driving Force Steering Wheels & Pedals". www.logitechg.com. Retrieved 2023-11-05. "Logitech G Driving Force Shifter for G29 and G920
Logitech_G29
Open standard for programming heterogenous computing systems, such as CPUs or GPUs
an OpenCL device are called "kernels". A single compute device typically consists of several compute units, which in turn comprise multiple processing
OpenCL
Interactions between groups of atoms that do not arise from chemical bonds
of atoms or molecules per unit volume, the total van der Waals force is often computed based on the "microscopic theory" as the sum over all interacting
Van_der_Waals_force
International Society for Computing
The Association for Computing Machinery (ACM) is an international learned society for computing founded on September 15, 1947, and headquartered in New
Association for Computing Machinery
Association_for_Computing_Machinery
GPU microarchitecture by AMD
instructions per cycle. It can contain up to 96 graphics Compute Units that can provide up to 61 TFLOPS of compute. While RDNA 3 include dedicated execution units
RDNA_3
FORCING COMPUTABILITY
FORCING COMPUTABILITY
Girl/Female
Tamil
Prajisha | பà¯à®°à®œà¯€à®·à®¾Â
Morning
Prajisha | பà¯à®°à®œà¯€à®·à®¾Â
Girl/Female
Tamil
Prattysha | பà¯à®°à®¤à¯à®¤à¯à®¯à®·à®¾
Morning
Prattysha | பà¯à®°à®¤à¯à®¤à¯à®¯à®·à®¾
Boy/Male
Latin
Strong; fortunate.
Boy/Male
Tamil
Morning
Girl/Female
Hindu, Indian
Forming the Crest
Surname or Lastname
English (Somerset)
English (Somerset) : unexplained.
Girl/Female
Tamil
Morning
Surname or Lastname
English
English : patronymic from Dear 1.German (Döring) : see Doering.
Girl/Female
Arabic, Muslim
Golden Morning; Beautiful Morning
Boy/Male
French, German
Renowned Warrior's Son; From Lorraine; Son of the Famous Warrior
Surname or Lastname
English
English : habitational name from a place in West Sussex, so named from the Old English personal name Fēra + -ingas ‘people of’, ‘family of’, or ‘followers of’.
Girl/Female
English Latin
Girl/Female
American, British, English, Latin
Farmer; Variant of Georgina
Surname or Lastname
English
English : from a diminutive of Moore 2, 3.North German (Möring) : patronymic from the nickname Mohr (see Mohr 2).North German (Möring) : habitational name from Möringen or Möhringen near Stendal and Stettin.Dutch : variant of Morin.
Boy/Male
German French
Famous in battle.
Surname or Lastname
English
English : habitational name from places in Oxfordshire and West Sussex named Goring, from Old English GÄringas ‘people of GÄra’, a short form of the various compound names with the first element gÄr ‘spear’.German (Göring) : see Goering.
Surname or Lastname
English
English : ethnic name from Old French Lohereng ‘man from Lorraine’ (see Lorraine).
Girl/Female
Tamil
Pratushya | பà¯à®°à®¤à¯à®‚à®·à¯à®¯à®¾Â
Morning
Pratushya | பà¯à®°à®¤à¯à®‚à®·à¯à®¯à®¾Â
Boy/Male
German
Renowned Warrior's Son
Surname or Lastname
English (mainly Lancashire and Cheshire)
English (mainly Lancashire and Cheshire) : unexplained.Probably an altered form of German Dornig, which is probably a nickname for someone with a sharp tongue, from an adjectival derivative of Middle High German, Middle Low German dorn ‘thorn’. The suffixes -ig and -ing were often interchanged in Pennsylvania German and elsewhere. The name may also refer to a sloe bush.
FORCING COMPUTABILITY
FORCING COMPUTABILITY
Surname or Lastname
English
English : variant spelling of Turpin.
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Telugu
One who Helps People; Lord Vishnu
Boy/Male
African, Arabic
Far
Boy/Male
Australian, German, Hebrew, Jewish
Warrior-hero; Tree Cutter; Feller; Hewer
Surname or Lastname
English (common in West Yorkshire)
English (common in West Yorkshire) : habitational name from Hainworth in West Yorkshire, named from the Old English personal name Hagena + Old English worð ‘enclosure’.English (common in West Yorkshire) : habitational name from Ainsworth in Lancashire, from the Old English personal name Ægen + worð ‘enclosure’. Names such as de Haynesworth and de Heynesworth occur in the surrounding area in the 14th century.
Boy/Male
Hindu, Indian, Traditional
Lord of Living Beings; Another Name for Vishnu
Girl/Female
American, Australian, British, Dutch, English, Finnish, French, German, Norse, Scandinavian, Swedish, Teutonic
Noble; Welfare; Battle Woman; Battle Stronghold; Ready for Battle; A Valkyrie; War
Girl/Female
Arabic, Muslim
Blond; Fair-haired; Fair-complexioned; Feminine of Ashqar
Boy/Male
Bengali, Indian
New Beginning
Surname or Lastname
English
English : unexplained. Perhaps an Anglicized form of French Perreault.
FORCING COMPUTABILITY
FORCING COMPUTABILITY
FORCING COMPUTABILITY
FORCING COMPUTABILITY
FORCING COMPUTABILITY
n.
The act of putting a foot to anything; also, that which is added as a foot; as, the footing of a stocking.
a.
Pertaining to agriculture; devoted to, adapted to, or engaged in, farming; as, farming tools; farming land; a farming community.
a.
Pertaining to, or characteristic of, working days, or workdays; everyday; hence, plodding; hard-working.
a.
Remote; distant; strange; not belonging; not connected; not pertaining or pertient; not appropriate; not harmonious; not agreeable; not congenial; -- with to or from; as, foreign to the purpose; foreign to one's nature.
n.
A piece of forged work in metal; -- a general name for a piece of hammered iron or steel.
n.
Stuffing; forcemeat.
n.
The art of raising plants, flowers, and fruits at an earlier season than the natural one, as in a hitbed or by the use of artificial heat.
a.
Outside; extraneous; separated; alien; as, a foreign country; a foreign government.
a.
Pertaining to the first part or early part of the day; being in the early part of the day; as, morning dew; morning light; morning service.
n.
See Furring.
p. pr. & vb. n.
of Fork
n.
The morning of yesterday.
n.
The act or process of giving form or shape to anything; as, in shipbuilding, the exact shaping of partially shaped timbers.
p. pr. & vb. n.
of Force
n.
The accomplishing of any purpose violently, precipitately, prematurely, or with unusual expedition.
v. i.
The aggregate of the fences put up for inclosure or protection; as, the fencing of a farm.
a.
Not native or belonging to a certain country; born in or belonging to another country, nation, sovereignty, or locality; as, a foreign language; foreign fruits.
p. pr. & vb. n.
of Form
p. pr. & vb. n.
of Farce
n.
The act of counterfeiting.