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 |

### "On the Consistency of New Foundations"

### Abstract

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.