An ordinal analysis of stability
- Michael RathjenAffiliated withDepartment of Pure Mathematics, University of Leeds Email author
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
This paper introduces an ordinal representation system based on ν-indescribable cardinals which is then employed for determining an upper bound for the proof–theoretic strength of the theory KPi+ ∀ρ ∃π π is π+ρ-stable, where KPi is KP augmented by the axiom saying that every set is contained in an admissible set.
- An ordinal analysis of stability
Archive for Mathematical Logic
Volume 44, Issue 1 , pp 1-62
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Michael Rathjen (1)
- Author Affiliations
- 1. Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, England