Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory...

In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification...

Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly...

the Foundations of Mathematics (German: Bemerkungen über die Grundlagen der Mathematik) is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics...

include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has...

Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types...

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function...

operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean...

lie at the Foundations of Geometry (1854) proposed new ideas about topology, and about basing mathematics (especially geometry) in terms of sets or manifolds...

needed] His Remarks on the Foundations of Mathematics contains his compiled views, notably a controversial repudiation of Gödel's incompleteness theorems...

I. The foundation of mathematics, Symposium on the foundations of mathematics Rudolf Carnap, The logicist foundations of mathematics, p. 41 Arend Heyting...

ISBN 978-0-619-21558-3. Pudlák, Pavel (2013). "Mathematical structures". Logical foundations of mathematics and computational complexity a gentle introduction. Cham: Springer...

perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century...

the sets of the formal languages that can be parsed by machines with limited computational power. In logic and the foundations of mathematics, formal languages...

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing...

modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all...

The Foundations of Mathematics, and other Essays, (ed.) R. B. Braithwaite Ramsey, F.P. (1978) Foundations – Essays in Philosophy, Logic, Mathematics and...

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article written by the physicist Eugene Wigner, published in Communication...

the foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor. Gödel's discoveries in the foundations of mathematics...

of Constructive Mathematics". Handbook of Mathematical Logic. 90: 973–1052. doi:10.1016/S0049-237X(08)71127-3 Bishop, Errett (1967). Foundations of Constructive...

Intuitionism maintains that the foundations of mathematics lie in the individual mathematician's intuition, thereby making mathematics into an intrinsically subjective...

of a function is a special case of a relation. In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to...

In mathematics, a codomain, counter-domain, or set of destination of a function is a set into which all of the output of the function is constrained to...

In mathematics and other fields, a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement....

In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map:...

of mathematics into axioms, and is studied in the foundations of mathematics. Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of...

theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined...

univalent foundations of mathematics and homotopy type theory. Vladimir Voevodsky's father, Aleksander Voevodsky, was head of the Laboratory of High Energy...