BETWEEN REDUCED POWERS AND ULTRAPOWERS, II

Ilijas Farah; Saharon Shelah

doi:10.1090/tran/8777

BETWEEN REDUCED POWERS AND ULTRAPOWERS, II

Ilijas Farah
, Saharon Shelah

Einstein Institute of Mathematics

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

Abstract

We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

Original language	English
Pages (from-to)	9007-9034
Number of pages	28
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	12
DOIs	https://doi.org/10.1090/tran/8777
State	Published - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society.

Keywords

Cohen model
Continuum Hypothesis
Proper Forcing Axiom
Ultrapowers
reduced powers
saturated models
small basis
universal models

Access to Document

10.1090/tran/8777

Cite this

@article{69eef6da05334ca2ac3dfd372d42efdd,

title = "BETWEEN REDUCED POWERS AND ULTRAPOWERS, II",

abstract = "We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fr{\'e}chet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.",

keywords = "Cohen model, Continuum Hypothesis, Proper Forcing Axiom, Ultrapowers, reduced powers, saturated models, small basis, universal models",

author = "Ilijas Farah and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

year = "2022",

month = dec,

doi = "10.1090/tran/8777",

language = "אנגלית",

volume = "375",

pages = "9007--9034",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "12",

}

TY - JOUR

T1 - BETWEEN REDUCED POWERS AND ULTRAPOWERS, II

AU - Farah, Ilijas

AU - Shelah, Saharon

PY - 2022/12

Y1 - 2022/12

N2 - We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

AB - We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

KW - Cohen model

KW - Continuum Hypothesis

KW - Proper Forcing Axiom

KW - Ultrapowers

KW - reduced powers

KW - saturated models

KW - small basis

KW - universal models

UR - https://www.scopus.com/pages/publications/85141723234

U2 - 10.1090/tran/8777

DO - 10.1090/tran/8777

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

AN - SCOPUS:85141723234

SN - 0002-9947

VL - 375

SP - 9007

EP - 9034

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 12

ER -

BETWEEN REDUCED POWERS AND ULTRAPOWERS, II

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this