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On a Question of Hamkins and Löwe on the modal logic of collapse
forcing
release_mge4taco2jd5dgpkic44xjstum
by
Mohammad Golshani, William Mitchell
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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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1609.02633v1
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