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39 relations: AD+, Antichain, Axiom of constructibility, Axiom of determinacy, Axiomatic system, Completeness (order theory), Continuum hypothesis, Countable chain condition, Countable set, Dense order, Diamond principle, Disjoint sets, Empty set, Forcing (mathematics), Georg Cantor, Greatest and least elements, Independence (mathematical logic), Infimum and supremum, Inner model, Interval (mathematics), Limit cardinal, List of statements independent of ZFC, Martin's axiom, Mathematics, Order isomorphism, Order topology, Real line, Regular cardinal, Ronald Jensen, Separable space, Set theory, Square principle, Successor cardinal, Superstrong cardinal, Suslin algebra, Suslin tree, Total order, Tree (set theory), Zermelo–Fraenkel set theory.
AD+
In set theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy.
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Antichain
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.
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Axiom of constructibility
The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible.
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Axiom of determinacy
In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962.
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Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
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Completeness (order theory)
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset).
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Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
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Countable chain condition
In order theory, a partially ordered set X is said to satisfy the countable chain condition, or to be ccc, if every strong antichain in X is countable.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Dense order
In mathematics, a partial order or total order.
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Diamond principle
In mathematics, and particularly in axiomatic set theory, the diamond principle is a combinatorial principle introduced by Ronald Jensen in that holds in the constructible universe and that implies the continuum hypothesis.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Greatest and least elements
In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S that is greater than every other element of S. The term least element is defined dually, that is, it is an element of S that is smaller than every other element of S. Formally, given a partially ordered set (P, ≤), an element g of a subset S of P is the greatest element of S if Hence, the greatest element of S is an upper bound of S that is contained within this subset.
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Independence (mathematical logic)
In mathematical logic, independence refers to the unprovability of a sentence from other sentences.
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Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
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Inner model
In set theory, a branch of mathematical logic, an inner model for a theory T is a substructure of a model M of a set theory that is both a model for T and contains all the ordinals of M.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Limit cardinal
In mathematics, limit cardinals are certain cardinal numbers.
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List of statements independent of ZFC
The mathematical statements discussed below are independent of ZFC (the Zermelo–Fraenkel axioms plus the axiom of choice, the canonical axiomatic set theory of contemporary mathematics), assuming that ZFC is consistent.
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Martin's axiom
In the mathematical field of set theory, Martin's axiom, introduced by, is a statement that is independent of the usual axioms of ZFC set theory.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Order isomorphism
In the mathematical field of order theory an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets).
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Order topology
In mathematics, an order topology is a certain topology that can be defined on any totally ordered set.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Regular cardinal
In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality.
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Ronald Jensen
Ronald Björn Jensen (born April 1, 1936) is an American mathematician active in Europe, primarily known for his work in mathematical logic and set theory.
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Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Square principle
In mathematical set theory, the global square principle is a combinatorial principle introduced by Ronald Jensen in his analysis of the fine structure of the constructible universe L.
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Successor cardinal
In the theory of cardinal numbers, we can define a successor operation similar to that in the ordinal numbers.
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Superstrong cardinal
In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j: V → M from V into a transitive inner model M with critical point κ and V_ ⊆ M. Similarly, a cardinal κ is n-superstrong if and only if there exists an elementary embedding j: V → M from V into a transitive inner model M with critical point κ and V_ ⊆ M. Akihiro Kanamori has shown that the consistency strength of an n+1-superstrong cardinal exceeds that of an n-huge cardinal for each n > 0.
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Suslin algebra
In mathematics, a Suslin algebra is a Boolean algebra that is complete, atomless, countably distributive, and satisfies the countable chain condition.
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Suslin tree
In mathematics, a Suslin tree is a tree of height ω1 such that every branch and every antichain is at most countable.
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Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
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Tree (set theory)
In set theory, a tree is a partially ordered set (T, \omega + 1.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Souslin conjecture, Souslin hypothesis, Souslin line, Souslin's hypothesis, Souslin's problem, Suslin Hypothesis, Suslin conjecture, Suslin hypothesis, Suslin line, Suslin problem, Suslin property, Suslin's hypothesis.
References
[1] https://en.wikipedia.org/wiki/Suslin's_problem
