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Axiom of choice and Axiom of constructibility

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

Difference between Axiom of choice and Axiom of constructibility

Axiom of choice vs. Axiom of constructibility

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty. The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible.

Similarities between Axiom of choice and Axiom of constructibility

Axiom of choice and Axiom of constructibility have 12 things in common (in Unionpedia): Axiom, Consistency, Constructible universe, Continuum hypothesis, Kurt Gödel, Large cardinal, Non-measurable set, Paul Cohen, Set theory, Springer Science+Business Media, Von Neumann–Bernays–Gödel set theory, Zermelo–Fraenkel set theory.

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 choice · Axiom and Axiom of constructibility · See more »

Consistency

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

Axiom of choice and Consistency · Axiom of constructibility and Consistency · See more »

Constructible universe

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 of choice and Constructible universe · Axiom of constructibility and Constructible universe · See more »

Continuum hypothesis

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

Axiom of choice and Continuum hypothesis · Axiom of constructibility and Continuum hypothesis · See more »

Kurt Gödel

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

Axiom of choice and Kurt Gödel · Axiom of constructibility and Kurt Gödel · See more »

Large cardinal

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

Axiom of choice and Large cardinal · Axiom of constructibility and Large cardinal · See more »

Non-measurable set

In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "size".

Axiom of choice and Non-measurable set · Axiom of constructibility and Non-measurable set · See more »

Paul Cohen

Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.

Axiom of choice and Paul Cohen · Axiom of constructibility and Paul Cohen · See more »

Set theory

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

Axiom of choice and Set theory · Axiom of constructibility and Set theory · See more »

Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Von Neumann–Bernays–Gödel set theory

In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC).

Axiom of choice and Von Neumann–Bernays–Gödel set theory · Axiom of constructibility and Von Neumann–Bernays–Gödel 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 choice and Zermelo–Fraenkel set theory · Axiom of constructibility and Zermelo–Fraenkel set theory · See more »

The list above answers the following questions

Axiom of choice and Axiom of constructibility Comparison

Axiom of choice has 173 relations, while Axiom of constructibility has 26. As they have in common 12, the Jaccard index is 6.03% = 12 / (173 + 26).

References

This article shows the relationship between Axiom of choice and Axiom of constructibility. To access each article from which the information was extracted, please visit:

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