Translator Disclaimer
2017 Two Upper Bounds on Consistency Strength of ¬ω and Stationary Set Reflection at Two Successive n
Martin Zeman
Notre Dame J. Formal Logic 58(3): 409-432 (2017). DOI: 10.1215/00294527-2017-0005

Abstract

We give modest upper bounds for consistency strengths for two well-studied combinatorial principles. These bounds range at the level of subcompact cardinals, which is significantly below a κ+-supercompact cardinal. All previously known upper bounds on these principles ranged at the level of some degree of supercompactness. We show that by using any of the standard modified Prikry forcings it is possible to turn a measurable subcompact cardinal into ω and make the principle ω,<ω fail in the generic extension. We also show that by using Lévy collapse followed by standard iterated club shooting it is possible to turn a subcompact cardinal into 2 and arrange in the generic extension that simultaneous reflection holds at 2, and at the same time, every stationary subset of 3 concentrating on points of cofinality ω has a reflection point of cofinality ω1.

Citation

Download Citation

Martin Zeman. "Two Upper Bounds on Consistency Strength of ¬ω and Stationary Set Reflection at Two Successive n." Notre Dame J. Formal Logic 58 (3) 409 - 432, 2017. https://doi.org/10.1215/00294527-2017-0005

Information

Received: 30 July 2012; Accepted: 31 December 2014; Published: 2017
First available in Project Euclid: 1 April 2017

zbMATH: 06761616
MathSciNet: MR3681102
Digital Object Identifier: 10.1215/00294527-2017-0005

Subjects:
Primary: 03E05
Secondary: 03E45, 03E55

Rights: Copyright © 2017 University of Notre Dame

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.58 • No. 3 • 2017
Back to Top