|Speaker:||Dr. Sergei TUPAILO, Institute of Cybernetics at TTU|
|Place:||Room B101, Institute of Cybernetics, Akadeemia tee 21, Tallinn, Estonia|
|Time:||Friday, September 24, 2004, 14:00|
New Foundations, NF, is a system of set theory named after Quine's 1937 article "New foundations for mathematical logic", where it was introduced. It was meant as a foundations of mathematics, alternative to Zermelo-Fraenkel set theory ZF and others. Obvious advantages of NF are that it's very easily formulated and many mathematical notions can be expressed in NF in a much more "natural" way than in ZF. However, in spite of efforts of many researches and many brilliant results, NF is still not known to be consistent relative to any theory in which we have reasonable confidence.
We investigate the possibility of reducing the Consis(NF) problem to consistency of various extensions of Jensen's NFU, "NF with Urelements", which is known to be consistent due to Jensen 1969. Extensions of NFU by different "large cardinal axioms" and their consistency strength have been studied by R. Jensen, S. Feferman, M. Boffa, R. Holmes, R. Solovay.