## Specker's proof of infinity in NF

Centro de Matemática e Aplicações Fundamentais

Universidade de Lisboa

Tuesday, 24 January 2012, 14:00 (note the unusual weekday)

Cybernetica Bldg (Akadeemia tee 21), room B101

Slides from the talk [pdf]

**Abstract**: We present Specker's 1953 result that NF refutes
the Axiom of Choice, with related fact that it proves the Axiom of
Infinity. All known proofs of these results are nontrivial, so there
is no surprise that neither Quine who introduced the theory in 1937,
nor anyone else, had noticed these facts before Specker.

Main reference:

E. Specker. The axiom of choice in Quine's new foundations for
mathematical logic. *Proceedings of the National Academy of Sciences
of the USA*, v. 39, pp. 972-975, 1953.

Tarmo Uustalu

Last update 25.1.2012