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In descriptive set theory, a set S {\displaystyle S} is said to be homogeneously Suslin if it is the projection of a homogeneous tree. S {\displaystyle
Homogeneously_Suslin_set
set Analytic set C-measurable set Projective set Inductive set Infinity-Borel set Suslin set Homogeneously Suslin set Weakly homogeneously Suslin set
List of properties of sets of reals
List_of_properties_of_sets_of_reals
Order whose elements are all comparable
partial order Ranking – Relationship between items in a set Suslin's problem – Problem in set theory Well-order – Class of mathematical orderings Let
Total_order
Mathematical concept
quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories. An equivalence relation on a set X {\displaystyle X}
Equivalence_class
Relationship between elements of two sets
symmetry of a homogeneous relation on a set where A = B . {\displaystyle A=B.} Commenting on the development of binary relations beyond homogeneous relations
Binary_relation
Maximal proper filter
In the mathematical field of set theory, an ultrafilter on a set X {\displaystyle X} is a maximal filter on the set X . {\displaystyle X.} In other words
Ultrafilter_on_a_set
Does the generalized continuum hypothesis imply the existence of an ℵ2-Suslin tree? If ℵω is a strong limit cardinal, is 2 ℵ ω < ℵ ω 1 {\displaystyle
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
all intersections of open sets in T with A. This construction is dual to the construction of the quotient topology. Suslin line T0 A space is T0 (or Kolmogorov)
Glossary_of_general_topology
Branch of mathematics
the subset order on a collection of sets: though the set of birds and the set of dogs are both subsets of the set of animals, neither the birds nor the
Order_theory
Euclidean space without distance and angles
In particular, every line bundle is trivial. More generally, the Quillen–Suslin theorem implies that every algebraic vector bundle over an affine space
Affine_space
Possible axiom for set theory
initial ordinals, and we have δ1 2n+2 = (δ1 2n+1)+, and for n < ω, the 2n-th Suslin cardinal is equal to δ1 2n−1. AD+ Axiom of real determinacy (ADR) Borel
Axiom_of_determinacy
Subfield of set theory
Descriptive Set Theory. North Holland. ISBN 978-0-444-70199-2. Woodin, W. Hugh (1988). "Supercompact cardinals, sets of reals, and weakly homogeneous trees"
Determinacy
Mathematical concept for comparing objects
relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only
Equivalence_relation
Would relate vector bundles over a regular Noetherian ring and over a polynomial ring
raised by Jean-Pierre Serre and was later proved by Quillen and Suslin; see Quillen–Suslin theorem. More generally, the conjecture was shown by Lindel (1981)
Bass–Quillen_conjecture
ideal theorem Ultrafilter Ultrafilter lemma Tree (set theory) Tree (descriptive set theory) Suslin's problem Absorption law Prewellordering Stone duality
List_of_order_theory_topics
Algebraic structure
to an analogy between projective modules and vector bundles. The Quillen–Suslin theorem asserts that any finitely generated projective module over k[T1
Commutative_ring
Weak form of the axiom of choice
in reverse mathematics that explores which set-theoretic axioms are needed to develop analysis. A homogeneous relation R {\displaystyle R} on X {\displaystyle
Axiom_of_dependent_choice
Hungarian and American mathematician and physicist (1903–1957)
but it is a proper class, not a set. Overall, von Neumann's major achievement in set theory was an "axiomatization of set theory and (connected with that)
John_von_Neumann
On polynomial rings over fields
result may be proven using Serre's theorem on regular local rings. Quillen–Suslin theorem Hilbert series and Hilbert polynomial D. Hilbert, Über die Theorie
Hilbert's_syzygy_theorem
algebra) Linear congruence theorem (number theory, modular arithmetic) Quillen–Suslin theorem (abstract algebra) Rédei's theorem (group theory) Schwartz–Zippel
List_of_theorems
Subject area in mathematics
higher K-theory of fields. Much later, it was discovered by Nesterenko and Suslin and by Totaro that Milnor K-theory is actually a direct summand of the true
Algebraic_K-theory
groups are actually equivalent. Schur algebras were used by Friedlander and Suslin to prove finite generation of cohomology of finite group schemes. The Schur
Schur_algebra
Tools for studying groups based on techniques from algebraic topology
(Brown 1972), Exercise III.1.3 (Knudson 2001), Chapter 4 (Brown 1972), §VI.9 Suslin, Andrei A. (1984), "Homology of GL n {\displaystyle \operatorname {GL} _{n}}
Group_cohomology
Uniqueness of countable dense linear orders
dense unbounded subset, it must be order-isomorphic to the real numbers. Suslin's problem asks whether orders having certain other properties of the order
Cantor's_isomorphism_theorem
Graduate-level textbooks in mathematics
Cycles, Transfers, and Motivic Homology Theories. Vladimir Voevodsky, Andrei Suslin, Eric M. Friedlander 2000-04-04 254 978-0691048154 144 The Real Fatou Conjecture
Annals_of_Mathematics_Studies
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HOMOGENEOUSLY SUSLIN-SET
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