On a Question of Hamkins and Löwe on the modal logic of collapse forcing release_mge4taco2jd5dgpkic44xjstum

by Mohammad Golshani, William Mitchell

Released as a article .

2016  

Abstract

Hamkins and Löwe asked whether there can be a model N of set theory with the property that N≡ N[H] whenever H is a generic collapse of a cardinal of N onto ω. We give a positive answer, assuming the existence of a cardinal κ with a measure sequence of length κ^+, a property which lies between o(κ)=κ^++ and o(κ)=κ^+++1. We also prove somewhat weaker lower bound for the consistency strength.
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Date   2016-09-09
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arXiv  1609.02633v1
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