Constructible universe and Inner model

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

Difference between Constructible universe and Inner model

Constructible universe vs. Inner model

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 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.

Axiom of regularity

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

Axiom of regularity and Constructible universe · Axiom of regularity and Inner model · See more »

Consistency

In classical deductive logic, a consistent theory is one that does not contain a contradiction.

Consistency and Constructible universe · Consistency and Inner model · See more »

Continuum hypothesis

In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.

Constructible universe and Continuum hypothesis · Continuum hypothesis and Inner model · See more »

Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

Constructible universe and Kurt Gödel · Inner model and Kurt Gödel · See more »

Measurable cardinal

In mathematics, a measurable cardinal is a certain kind of large cardinal number.

Constructible universe and Measurable cardinal · Inner model and Measurable cardinal · See more »

Minimal model (set theory)

In set theory, the minimal model is the minimal standard model of ZFC.

Constructible universe and Minimal model (set theory) · Inner model and Minimal model (set theory) · See more »

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.

Constructible universe and Ordinal number · Inner model and Ordinal number · See more »

Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

Constructible universe and Set theory · Inner model and Set theory · See more »

Transitive set

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

Constructible universe and Transitive set · Inner model and Transitive set · See more »

Well-founded relation

In mathematics, a binary relation, R, is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.

Constructible universe and Well-founded relation · Inner model and Well-founded relation · See more »

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.

Constructible universe and Zermelo–Fraenkel set theory · Inner model and Zermelo–Fraenkel set theory · See more »