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- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-004-0226-2
- Publisher site
- See Article on Publisher Site
Abstract
This paper is the first in a series of three which culminates in an ordinal analysis of Π1 2-comprehension. On the set-theoretic side Π1 2-comprehension corresponds to Kripke-Platek set theory, KP, plus Σ1-separation. The strength of the latter theory is encapsulated in the fact that it proves the existence of ordinals π such that, for all β>π, π is β-stable, i.e. L π is a Σ1-elementary substructure of L β . The objective of this paper is to give an ordinal analysis of a scenario of not too complicated stability relations as experience has shown that the understanding of the ordinal analysis of Π1 2-comprehension is greatly facilitated by explicating certain simpler cases first.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Sep 1, 2004