set-theoretic statement
41Compact element — In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non empty directed set that does not already contain members above the compact… …
42Hanna Neumann conjecture — In the mathematical subject of group theory, the Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was posed by Hanna Neumann in 1957Hanna Neumann. On… …
43Naturalized epistemology — is a collection of philosophic views concerned with the theory of knowledge that emphasize the role of natural scientific methods. This shared emphasis on scientific methods of studying knowledge shifts focus to the empirical processes of… …
44Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical …
45Axiom 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. Formal statement In the formal language of… …
46Logical positivism — (also known as logical empiricism, scientific philosophy, and neo positivism) is a philosophy that combines empiricism the idea that observational evidence is indispensable for knowledge with a version of rationalism incorporating mathematical… …
47Evenness of zero — The number 0 is even. There are several ways to determine whether an integer is even or odd, all of which indicate that 0 is an even number: it is a multiple of 2, it is evenly divisible by 2, it is surrounded on both sides by odd integers, and… …
48Constructivism (mathematics) — In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct ) a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption,… …
49Closure (topology) — For other uses, see Closure (disambiguation). In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are near S. A point which is in the… …
50Theory (mathematical logic) — This article is about theories in a formal language, as studied in mathematical logic. For other uses, see Theory (disambiguation). In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually… …
