TY - JOUR

T1 - Forcing a countable structure to belong to the ground model

AU - Kaplan, Itay

AU - Shelah, Saharon

N1 - Publisher Copyright:
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85007441197&partnerID=8YFLogxK

U2 - 10.1002/malq.201400094

DO - 10.1002/malq.201400094

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85007441197

SN - 0942-5616

VL - 62

SP - 530

EP - 546

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 6

ER -