Back to Search Start Over

A Model in Which Well-Orderings of the Reals First Appear at a Given Projective Level, Part III—The Case of Second-Order PA

Authors :
Vladimir Kanovei
Vassily Lyubetsky
Source :
Mathematics, Vol 11, Iss 15, p 3294 (2023)
Publication Year :
2023
Publisher :
MDPI AG, 2023.

Abstract

A model of set theory ZFC is defined in our recent research, in which, for a given n≥3, (An) there exists a good lightface Δn1 well-ordering of the reals, but (Bn) no well-orderings of the reals (not necessarily good) exist in the previous class Δn−11. Therefore, the conjunction (An)∧(Bn) is consistent, modulo the consistency of ZFC itself. In this paper, we significantly clarify and strengthen this result. We prove the consistency of the conjunction (An)∧(Bn) for any given n≥3 on the basis of the consistency of PA2, second-order Peano arithmetic, which is a much weaker assumption than the consistency of ZFC used in the earlier result. This is a new result that may lead to further progress in studies of the projective hierarchy.

Details

Language :
English
ISSN :
22277390
Volume :
11
Issue :
15
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.82f6425350a642e3b3a20c5916f1ed6f
Document Type :
article
Full Text :
https://doi.org/10.3390/math11153294