26 relations: Analytical hierarchy, Axiom, Axiom of choice, Cabal (set theory), Consistency, Constructible universe, Continuum hypothesis, Equiconsistency, Erdős cardinal, Inner model theory, Kurt Gödel, Large cardinal, List of large cardinal properties, Mathematical Association of America, Measurable cardinal, Non-measurable set, Paul Cohen, Saharon Shelah, Set theory, Springer Science+Business Media, Statements true in L, Suslin's problem, Von Neumann universe, Von Neumann–Bernays–Gödel set theory, Zermelo–Fraenkel set theory, Zero sharp.
In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy.
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.
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 Cabal was, or perhaps is, a set of set theorists in Southern California, particularly at UCLA and Caltech, but also at UC Irvine.
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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 mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.
In mathematics, an Erdős cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by.
In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof.
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
This page includes a list of cardinals with large cardinal properties.
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.
In mathematics, a measurable cardinal is a certain kind of large cardinal number.
In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "size".
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.
Saharon Shelah (שהרן שלח) is an Israeli mathematician.
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.
Here is a list of propositions that hold in the constructible universe (denoted L).
In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
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.
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).
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.
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.