Forcing a countable structure to belong to the ground model

Itay Kaplan, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)530-546
Number of pages17
JournalMathematical Logic Quarterly
Volume62
Issue number6
DOIs
StatePublished - 1 Dec 2016

All Science Journal Classification (ASJC) codes

  • Logic

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