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

Remarks on the Foundations of Mathematics (‹See Tfd›German: Bemerkungen über die Grundlagen der Mathematik) is a book of Ludwig Wittgenstein's notes on...

Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major...

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

theory at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program. Institute for Advanced Study. Frank Ruda...

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

rigor and more abstract foundations, some proposed defining mathematics purely in terms of deduction and logic: Mathematics is the science that draws...

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