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

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

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

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

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

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

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...

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

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

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

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

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

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...

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...

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...

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

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...

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

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...

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

how to repair it. Philosophy portal Mathematics portal Ackermann coding Foundations of mathematics New Foundations Anderson, D. J., and Edward Zalta, 2004...

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...

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

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...

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

Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics...

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....

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

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...