Axiom of pairing and Constructible universe

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

Difference between Axiom of pairing and Constructible universe

Axiom of pairing vs. Constructible universe

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

Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

Axiom and Axiom of pairing · Axiom and Constructible universe · See more »

Axiom of empty set

In axiomatic set theory, the axiom of empty set is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or without the axiom of choice.

Axiom of empty set and Axiom of pairing · Axiom of empty set and Constructible universe · See more »

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 Axiom of pairing · Axiom of extensionality and Constructible universe · See more »

Axiom of infinity

In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory.

Axiom of infinity and Axiom of pairing · Axiom of infinity and Constructible universe · See more »

Axiom of power set

In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.

Axiom of pairing and Axiom of power set · Axiom of power set and Constructible universe · See more »

Axiom of union

In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory.

Axiom of pairing and Axiom of union · Axiom of union and Constructible universe · See more »

Axiom schema of replacement

In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.

Axiom of pairing and Axiom schema of replacement · Axiom schema of replacement and Constructible universe · See more »

Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.

Axiom of pairing and Formal language · Constructible universe and Formal language · See more »

Hereditarily finite set

In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets.

Axiom of pairing and Hereditarily finite set · Constructible universe and Hereditarily finite set · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Axiom of pairing and Mathematics · Constructible universe and Mathematics · See more »

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

Axiom of pairing and Set (mathematics) · Constructible universe and Set (mathematics) · See more »

Set theory

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

Axiom of pairing and Set theory · Constructible universe and Set theory · 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.

Axiom of pairing and Zermelo–Fraenkel set theory · Constructible universe and Zermelo–Fraenkel set theory · See more »