In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NFU, an important variant of NF due to Jensen (1969) and exposited in Holmes (1998).
Read more about New Foundations: The Type Theory TST, Finite Axiomatizability, Cartesian Closure, The Consistency Problem and Related Partial Results, How NF(U) Avoids The Set-theoretic Paradoxes, Models of NFU, Strong Axioms of Infinity
Famous quotes containing the word foundations:
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)