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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. [1]

## Analytical hierarchy

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy.

## 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 of choice

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.

## Cabal (set theory)

The Cabal was, or perhaps is, a set of set theorists in Southern California, particularly at UCLA and Caltech, but also at UC Irvine.

## Consistency

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

## 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.

## Continuum hypothesis

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

## Equiconsistency

In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.

## Erdős cardinal

In mathematics, an Erdős cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by.

## Inner model theory

In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof.

## Kurt Gödel

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

## Large cardinal

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

## Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

## Measurable cardinal

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

## Non-measurable set

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

## Paul Cohen

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

## Saharon Shelah

Saharon Shelah (שהרן שלח) is an Israeli mathematician.

## Set theory

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

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.

## Statements true in L

Here is a list of propositions that hold in the constructible universe (denoted L).

## Suslin's problem

In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.

## 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.

## 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).

## 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.

## Zero sharp

In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe.

## References

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