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Square principles with tail-end agreement

Square principles with tail-end agreement This paper investigates the principles $${\square^{{{\rm ta}}}_{\lambda,\delta}}$$ □ λ , δ ta , weakenings of $${\square_\lambda}$$ □ λ which allow $${\delta}$$ δ many clubs at each level but require them to agree on a tail-end. First, we prove that $${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$ □ λ , < ω ta implies $${\square_\lambda}$$ □ λ . Then, by forcing from a model with a measurable cardinal, we show that $${\square_{\lambda,2}}$$ □ λ , 2 does not imply $${\square^{{\rm{ta}}}_{\lambda,\delta}}$$ □ λ , δ ta for regular $${\lambda}$$ λ , and $${\square^{{\rm{ta}}}_{\delta^+,\delta}}$$ □ δ + , δ ta does not imply $${\square_{\delta^+,< \delta}}$$ □ δ + , < δ . With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that $${\square^{{\rm {ta}}}_{\lambda,\delta}}$$ □ λ , δ ta does not imply $${\square_{\lambda,< \delta}}$$ □ λ , < δ for $${\delta < \lambda}$$ δ < λ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Square principles with tail-end agreement

Chen, William; Neeman, Itay
Archive for Mathematical Logic , Volume 54 (4) – Feb 1, 2015
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-015-0419-x
Publisher site
See Article on Publisher Site

Abstract

This paper investigates the principles $${\square^{{{\rm ta}}}_{\lambda,\delta}}$$ □ λ , δ ta , weakenings of $${\square_\lambda}$$ □ λ which allow $${\delta}$$ δ many clubs at each level but require them to agree on a tail-end. First, we prove that $${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$ □ λ , < ω ta implies $${\square_\lambda}$$ □ λ . Then, by forcing from a model with a measurable cardinal, we show that $${\square_{\lambda,2}}$$ □ λ , 2 does not imply $${\square^{{\rm{ta}}}_{\lambda,\delta}}$$ □ λ , δ ta for regular $${\lambda}$$ λ , and $${\square^{{\rm{ta}}}_{\delta^+,\delta}}$$ □ δ + , δ ta does not imply $${\square_{\delta^+,< \delta}}$$ □ δ + , < δ . With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that $${\square^{{\rm {ta}}}_{\lambda,\delta}}$$ □ λ , δ ta does not imply $${\square_{\lambda,< \delta}}$$ □ λ , < δ for $${\delta < \lambda}$$ δ < λ .

Journal

Archive for Mathematical Logic – Springer Journals

Published: Feb 1, 2015

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