Forcing a countable structure to belong to the ground model

Itay Kaplan; Saharon Shelah

doi:10.1002/malq.201400094

Forcing a countable structure to belong to the ground model

Itay Kaplan^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Suppose that P is a forcing notion, L is a language (in V), (Formula presented.) a P-name such that (Formula presented.) “(Formula presented.) is a countable L-structure”. In the product P × P, there are names (Formula presented.) such that for any generic filter G = G₁ × G₂ over P × P, (Formula presented.) and (Formula presented.). Zapletal asked whether or not (Formula presented.) implies that there is some M ∈ V such that (Formula presented.). We answer this question negatively and discuss related issues.

Original language	English
Pages (from-to)	530-546
Number of pages	17
Journal	Mathematical Logic Quarterly
Volume	62
Issue number	6
DOIs	https://doi.org/10.1002/malq.201400094
State	Published - 1 Dec 2016

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© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Forcing a countable structure to belong to the ground model

Abstract

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