The consistency of a club-guessing failure at the successor of a regular cardinal

Aspero, David (2014) The consistency of a club-guessing failure at the successor of a regular cardinal. In: Infinity, computability, and metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch. College Publications, London, pp. 5-27. ISBN 1848901305

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Abstract

I answer a question of Shelah by showing that if $\k$ is a regular cardinal such that $2^{{<}\k}=\k$, then there is a ${<}\k$--closed partial order preserving cofinalities and forcing that for every club--sequence $\la C_\d\mid \d\in \k^+\cap\cf(\k)\ra$ with $\ot(C_\d)=\k$ for all $\d$ there is a club $D\sub\k^+$ such that $\{\a<\k\mid \{C_\d(\a+1), C_\d(\a+2)\}\sub D\}$ is bounded for every $\d$. This forcing is built as an iteration with ${<}\k$--supports and with symmetric systems of submodels as side conditions.

Item Type:	Book Section
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Pure Connector
Date Deposited:	09 Jul 2014 12:06
Last Modified:	27 Nov 2024 09:59
URI:	https://ueaeprints.uea.ac.uk/id/eprint/49358
DOI:

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