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
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AN - SCOPUS:85007441197
SN - 0942-5616
VL - 62
SP - 530
EP - 546
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 6
ER -