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Constructible universe and Ordinal definable set

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Constructible universe and Ordinal definable set

Constructible universe vs. Ordinal definable set

In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets. In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first order formula.

Similarities between Constructible universe and Ordinal definable set

Constructible universe and Ordinal definable set have 9 things in common (in Unionpedia): Axiom of constructibility, Axiom of extensionality, Class (set theory), Inner model, Large cardinal, Ordinal number, Set theory, Transitive set, Von Neumann universe.

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 extensionality

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory.

Axiom of extensionality and Constructible universe · Axiom of extensionality and Ordinal definable set · See more »

Class (set theory)

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.

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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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Large cardinal

In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.

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Ordinal number

In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.

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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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Transitive set

In set theory, a set A is called transitive if either of the following equivalent conditions hold.

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Von Neumann universe

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets.

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The list above answers the following questions

Constructible universe and Ordinal definable set Comparison

Constructible universe has 66 relations, while Ordinal definable set has 14. As they have in common 9, the Jaccard index is 11.25% = 9 / (66 + 14).

References

This article shows the relationship between Constructible universe and Ordinal definable set. To access each article from which the information was extracted, please visit:

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