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

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...

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

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...

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...

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

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...

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

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

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...

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

Mathematical Foundations of Quantum Mechanics (German: Mathematische Grundlagen der Quantenmechanik) is a quantum mechanics book written by John von Neumann...

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

Department of Mathematics and Statistics at the University of Helsinki. Her main research interests are mathematical logic and the foundations of mathematics. In...

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

Keisler, H. Jerome (1990), Model Theory, Studies in Logic and the Foundations of Mathematics (3rd ed.), Elsevier, ISBN 978-0-444-88054-3 Hodges, Wilfrid (1997)...

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....

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...

mathematics and logic are identical. The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported...

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

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...

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

ISBN 9780821847619. Mayberry, John P. (2000), The Foundations of Mathematics in the Theory of Sets, Encyclopedia of Mathematics and its Applications, vol. 82, Cambridge...

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

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

there the predictions of quantum field theory are exceptionally successful. The inward face looked at mathematical foundations and found inconsistency...