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Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
mean superset. Quine, W.V. (1981): Mathematical Logic, §6 Hintikka, Jaakko (1998), The Principles of Mathematics Revisited, Cambridge University Press
List_of_logic_symbols
Non-contradiction of a theory
François (2019). A First Journey through Logic. Student Mathematical Library. Vol. 89. American Mathematical Society. p. 63. ISBN 9781470452728. This
Consistency
Set of sentences in a formal language
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first
Theory_(mathematical_logic)
Mapping of mathematical formulas to a particular meaning
model theory; see interpretation (model theory). In the context of mathematical logic, the term "model" was first used in 1940 by the philosopher Willard
Structure (mathematical logic)
Structure_(mathematical_logic)
Class of formal logics
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had
Classical_logic
Entscheidungsproblem" Introduction to Mathematical Philosophy "New Foundations for Mathematical Logic" Principia Mathematica The Simplest Mathematics History and philosophy
Philosophy_of_mathematics
School of thought in philosophy of mathematics
is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and
Logicism
System of formal mathematical logic
foundation for mathematics comparable to first-order logic plus set theory. It is a form of higher-order logic and closely related to the logics of the HOL
Q0_(mathematical_logic)
Type of logical system
In mathematics, philosophy, linguistics, and computer science, first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational
First-order_logic
proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period
History_of_logic
In logic, a statement which is always true
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,
Tautology_(logic)
Sequence of words formed by specific rules
power. In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism
Formal_language
Term in mathematical logic
In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences. The sentences in this set
Independence (mathematical logic)
Independence_(mathematical_logic)
Overview of and topical guide to logic
calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal instantiation
Outline_of_logic
Theorem for proving more complex theorems
J. (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics. p. 16. ISBN 0-89871-420-6. "Definition
Lemma_(mathematics)
timeline of mathematical logic; see also history of logic. 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what
Timeline of mathematical logic
Timeline_of_mathematical_logic
In mathematical logic, a well-formed formula with no free variables
In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence
Sentence_(mathematical_logic)
Symbol representing a property or relation in logic
Igor Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122
Predicate_(logic)
Study of correct reasoning
addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or
Logic
Basic notion of sameness in mathematics
mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic, which studies formal logic within
Equality_(mathematics)
Logical connective AND
In logic, mathematics and linguistics, and ( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical
Logical_conjunction
that mathematical statements are useful fictions that do not correspond to any actual abstract objects. Logicism asserts that all mathematical truths
Mathematical_object
Field of knowledge
The relationship between mathematical truth, logic, and reality is a subject of philosophical debate. Some areas of mathematics, such as game theory, are
Mathematics
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
British mathematician and logician (1806–1871)
for coining the term "mathematical induction", the underlying principles of which he formalized. De Morgan's contributions to logic are heavily used in
Augustus_De_Morgan
Statement in a metalanguage
In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order
Judgment_(mathematical_logic)
German mathematician (1912–2003)
contributions to the foundations of mathematical logic. Hermes was born in Neunkirchen. From 1931, he studied mathematics, physics, chemistry, biology and
Hans_Hermes
In mathematics, a statement that has been proven
important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them
Theorem
Reasoning about equations with free variables
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic
Algebraic_logic
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
System for reasoning about vagueness
identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. A basic
Fuzzy_logic
Form of mathematical proof
used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction
Mathematical_induction
Algebraic manipulation of "true" and "false"
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the
Boolean_algebra
theory List of graph theory topics Logic is the foundation that underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning
Lists_of_mathematics_topics
Axiomatic set theory devised by W.V.O. Quine
In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification
New_Foundations
Basic framework of mathematics
foundational crisis of mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set
Foundations_of_mathematics
This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and
List of mathematical logic topics
List_of_mathematical_logic_topics
Mathematical use of "for all" and "there exists"
In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of
Quantifier_(logic)
Argument whose conclusion must be true if its premises are
the framework of classical logic. However, within that system 'true' and 'false' essentially function more like mathematical states such as binary 1s and
Validity_(logic)
Book by Wilhelm Ackermann
Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge
Principles of Mathematical Logic
Principles_of_Mathematical_Logic
Logical connective OR
(2016). Introduction to Mathematical Logic. WORLD SCIENTIFIC. p. 150. doi:10.1142/9783. ISBN 978-9814343879. Howson, Colin (1997). Logic with trees: an introduction
Logical_disjunction
American mathematician (1900-1982)
physics, earning a Master of Arts (M.A.) in 1924. Curry's interest in mathematical logic began during this period when he was introduced to the Principia Mathematica
Haskell_Curry
theorem (mathematical logic) Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic)
List_of_theorems
Mathematical model for deduction or proof systems
1967. Mathematical Logic Reprinted by Dover, 2002. ISBN 0-486-42533-9. Smullyan, Raymond M., 1961. Theory of Formal Systems: Annals of Mathematics Studies
Formal_system
Method of deriving conclusions
proof by contradiction, and mathematical induction. Mathematical logic, a subfield of mathematics and logic, uses mathematical methods and frameworks to
Rule_of_inference
Limitative results in mathematical logic
published by Kurt Gödel in 1931, are important both in mathematical logic and in philosophy of mathematics. The theorems are interpreted as showing that Hilbert's
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Statement that is taken to be true
Modern mathematics formalizes its foundations to such an extent that mathematical theories can be regarded as mathematical objects, and mathematics itself
Axiom
Type of formal logic
Press. —— (1993) Mathematics of Modality, CSLI Lecture Notes No. 43. University of Chicago Press. —— (2006) "Mathematical Modal Logic: a View of its Evolution"
Modal_logic
Impossible task in computing
(1951), "Review of Foundations of mathematics and mathematical logic by S. A. Yanovskaya", Journal of Symbolic Logic, 16 (1): 46–48, doi:10.2307/2268665
Entscheidungsproblem
Symbol representing a mathematical concept
In formal systems particularly mathematical logic, a function symbol is a non-logical symbol which represents a function or mapping on the domain of discourse
Function_symbol
Academic discipline
validate and discover new mathematical theorems and proofs. There has always been a strong influence from mathematical logic on the field of artificial
Logic_in_computer_science
In mathematical logic, an atomic formula or its negation
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. The definition mostly appears in proof
Literal_(mathematical_logic)
Concept in model theory
systems of formal logic can be defined via model theory. Specifically, a logic α {\displaystyle \alpha } is said to be as strong as a logic β {\displaystyle
Strength_(mathematical_logic)
Logical formalism using combinators instead of variables
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell
Combinatory_logic
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Description of non-logical symbols
In mathematical logic, a signature is a description of the non-logical symbols of a formal language. In universal algebra, a signature lists the operations
Signature_(logic)
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
the applications of formal logic to mathematics. Mathematical optimization Mathematical physics The development of mathematical methods suitable for application
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
Formal semantics based on algebras
In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4
Algebraic semantics (mathematical logic)
Algebraic_semantics_(mathematical_logic)
Book by Bertrand Russell
deals with a wide variety of topics within the philosophy of mathematics and mathematical logic including the logical basis and definition of natural numbers
Introduction to Mathematical Philosophy
Introduction_to_Mathematical_Philosophy
Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes
Propositional_logic
Concept in mathematical logic
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the
Converse_(logic)
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Concept in model theory
In model theory, a branch of mathematical logic, the diagram of a structure is the set of sentences with parameters from the structure that are true in
Diagram_(mathematical_logic)
International specialist organization
Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in
Association for Symbolic Logic
Association_for_Symbolic_Logic
Branch of logic using category theory to study mathematical structures
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also
Categorical_logic
Mathematical term; concerning axioms used to derive theorems
Formal system – Mathematical model for deduction or proof systems Gödel's incompleteness theorems – Limitative results in mathematical logic Hilbert-style
Axiomatic_system
American mathematician (1927–2000)
memory. Mathematical Logic, Addison Wesley 1967, 2nd edition, Association for Symbolic Logic, 2001 Degrees of unsolvability, North Holland Mathematical Studies
Joseph_R._Shoenfield
Symbolic description of a mathematical object
expression. For a non-formalized language, that is, in most mathematical texts outside of mathematical logic, for an individual expression it is not always possible
Expression_(mathematics)
Study of mathematics itself
study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories
Metamathematics
Theory of logic to account for observations from quantum theory
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions
Quantum_logic
Puzzle deriving from the mathematical field of deduction
A logic puzzle is a puzzle deriving from the mathematical field of deduction. The logic puzzle was first produced by Charles Lutwidge Dodgson, who is
Logic_puzzle
3-volume treatise on mathematics, 1910–1913
methods of mathematical logic and to minimise the number of primitive notions, axioms, and inference rules; to precisely express mathematical propositions
Principia_Mathematica
Collection of mathematical objects
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects:
Set_(mathematics)
Function that is its own inverse
Providence, RI: American Mathematical Society, ISBN 0-8218-0904-0, Zbl 0955.16001 "Involution", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Media
Involution_(mathematics)
Mathematical logic concept
In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula
Atomic_formula
Mathematical use of "there exists"
Sheaves in Geometry and Logic Springer-Verlag ISBN 0-387-97710-4. See p. 58. Hinman, P. (2005). Fundamentals of Mathematical Logic. A K Peters. ISBN 1-56881-262-0
Existential_quantification
True when either but not both inputs are true
Introduction to Mathematical Logic (3 ed.). New York, Dordrecht, Heidelberg and London: Springer. p. 3. Ladd, Christine (1883). "On the Algebra of Logic". In Peirce
Exclusive_or
Symbol representing a mathematical object
In mathematics, a variable (from Latin variabilis 'changeable') is a symbol, typically a letter, that refers to an unspecified mathematical object. One
Variable_(mathematics)
Study of the properties of logical systems
interpretations. The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory, and the study of deductive systems
Metalogic
numbers that have important applications in mathematical logic. They are a standard topic in mathematical logic textbooks such as Soare (1987) and Rogers
Creative_and_productive_sets
differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Academic journal
Archive for Mathematical Logic is a peer-reviewed mathematics journal published by Springer Science+Business Media. It was established in 1950 and publishes
Archive for Mathematical Logic
Archive_for_Mathematical_Logic
Logical incompatibility between two or more propositions
McKubre-Jordens, 2020. Classifying Material Implications over Minimal Logic. Archive for Mathematical Logic 59 (7-8):905-924. Pakin, Scott (January 19, 2017). "The
Contradiction
System of formal deduction in logic
Combinatory Logic Vol. I. Vol. 1. Amsterdam: North Holland. Monk, J. Donald (1976). Mathematical Logic. Graduate Texts in Mathematics. Berlin, New York:
Hilbert_system
branch of mathematics that studies mathematical systems and theories from a higher-level perspective, often using methods from mathematical logic. metatheorem
Glossary_of_logic
Algebraization of first-order logic
In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic
Predicate_functor_logic
Concept in logic
instantiation) For a non-formalized language, that is, in most mathematical texts outside of mathematical logic, for an individual expression it is not always possible
Substitution_(logic)
Overview of and topical guide to discrete mathematics
list of mathematical terms; just a selection of typical terms of art that may be encountered. Logic – Study of correct reasoning Modal logic – Type of
Outline of discrete mathematics
Outline_of_discrete_mathematics
Term in logic and deductive reasoning
deductive reasoning contexts and the latter arises in metalogic and mathematical logic. In deductive reasoning, a sound argument is an argument that is valid
Soundness
be mathematically characterized in terms of all its possible behaviors (including those involving unbounded nondeterminism). So mathematical logic can
Indeterminacy in concurrent computation
Indeterminacy_in_concurrent_computation
1931 paper by Kurt Gödel
Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Submitted November 17, 1930, it was originally published
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems
Symbol connecting formulas in logic
Louis Nebert. p. 10. Russell (1908) Mathematical logic as based on the theory of types (American Journal of Mathematics 30, p222–262, also in From Frege
Logical_connective
Symbol in mathematical logic
In mathematical logic and computer science the symbol ⊢ ( ⊢ {\displaystyle \vdash } ) has taken the name turnstile because of its resemblance to a typical
Turnstile_(symbol)
Formal system of logic
In mathematics and logic, a higher-order logic (HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes
Higher-order_logic
Whether a decision problem has an effective method to derive the answer
"Introduction to first-order logic", in Barwise, Jon (ed.), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland
Decidability_(logic)
nature of mathematics and individual mathematical problems into the future is a widely debated topic; many past predictions about modern mathematics have been
Future_of_mathematics
Logical operation
2020. "Logic and Mathematical Statements - Worked Examples". www.math.toronto.edu. Retrieved 2 September 2020. Beall, Jeffrey C. (2010). Logic: the basics
Negation
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MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Telugu
An Astrologer; Mathematician
Girl/Female
Indian
Successful; Logical Thinkers
Boy/Male
Tamil
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Tamil
Viviktha | விவீகà¯à®¤à®¾Â
Distinguished, Pure, Deep, Logically intelligent
Viviktha | விவீகà¯à®¤à®¾Â
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Boy/Male
Hindu
Full of feathers, Full of logic, Name of sage, Vatsyayan
Girl/Female
Arabic, Muslim, Pashtun
Logic; Reason
Girl/Female
Gujarati, Hindu, Indian, Kannada, Telugu
Mathematician
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Tamil
Vivikta | விவிகதா
Distinguished, Pure, Deep, Logically intelligent
Vivikta | விவிகதா
Boy/Male
Indian
Intelligent, Logical
Girl/Female
Hindu
Distinguished, Pure, Deep, Logically intelligent
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Girl/Female
Hindu
Mathematician
Surname or Lastname
English
English : habitational name from a place in West Yorkshire named Colden, from Old English cald ‘cold’ col ‘charcoal’ + denu ‘valley’.English and Scottish : variant of Cowden.Cadwallader Colden (1688–1778), physician, botanist, and mathematician, who for fifteen years was lieutenant-governor of New York colony, was born in Dalkeith, Scotland.
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Girl/Female
Tamil
Mathematician
Boy/Male
Bengali, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
One who Calculates; Astrologer; Mathematician
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
MATHEMATICAL LOGIC
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