set-theoretic statement
11Class (set theory) — In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) which can be unambiguously defined by a property that all its members share. The precise definition of class… …
12Internal set theory — (IST) is a mathematical theory of sets developed by Edward Nelson which provides an axiomatic basis for a portion of the non standard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, the axioms… …
13Constructive set theory — is an approach to mathematical constructivism following the program of axiomatic set theory. That is, it uses the usual first order language of classical set theory, and although of course the logic is constructive, there is no explicit use of… …
14Diophantine set — In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk)=0 (usually abbreviated P(x,y)=0 ) where P(x,y) is a polynomial with integer coefficients. A Diophantine set is a subset S of Nj [1] so that for some… …
15Equiconsistency — In mathematical logic, two theories are equiconsistent if, roughly speaking, they are as consistent as each other . It is not in general possible to prove the absolute consistency of a theory T. Instead we usually take a theory S, believed to be… …
16Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …
17Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …
18logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher …
19Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …
20Algebra of sets — The algebra of sets develops and describes the basic properties and laws of sets, the set theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures …
