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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-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 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

All Science Journal Classification (ASJC) codes

Logic

Access to Document

10.1002/malq.201400094

Cite this

@article{96b6afff93194610a8ba9246db177fa4,

title = "Forcing a countable structure to belong to the ground model",

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.",

author = "Itay Kaplan and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim",

year = "2016",

month = dec,

day = "1",

doi = "10.1002/malq.201400094",

language = "الإنجليزيّة",

volume = "62",

pages = "530--546",

journal = "Mathematical Logic Quarterly",

issn = "0942-5616",

publisher = "Wiley-VCH Verlag",

number = "6",

}

TY - JOUR

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

AU - Kaplan, Itay

AU - Shelah, Saharon

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 - مقالة

SN - 0942-5616

VL - 62

SP - 530

EP - 546

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 6

ER -

Forcing a countable structure to belong to the ground model

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this