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LIFTING PROOF THEORY TO THE COUNTABLE ORDINALS: ZERMELO-FRAENKEL SET THEORY

Published online by Cambridge University Press:  25 June 2014

TOSHIYASU ARAI
TOSHIYASU ARAI*
Affiliation:
GRADUATE SCHOOL OF SCIENCE CHIBA UNIVERSITY CHIBA, 263-8522, JAPANE-mail: tosarai@faculty.chiba-u.jp
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Abstract

We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound on definable countable ordinals in Zermelo-Fraenkel set theory ZF.

Keywords

Provably countableSkolem hullcollapsing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 2 , June 2014 , pp. 325 - 354
Copyright
Copyright © The Association for Symbolic Logic 2014 

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