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ELEMENTARY EQUIVALENCE IN POSITIVE LOGIC VIA PRIME PRODUCTS

Part of: Model theory

Published online by Cambridge University Press:  05 July 2023

TOMMASO MORASCHINI Open the ORCID record for TOMMASO MORASCHINI [Opens in a new window] ,
JOHANN J. WANNENBURG Open the ORCID record for JOHANN J. WANNENBURG [Opens in a new window]  and
KENTARO YAMAMOTO Open the ORCID record for KENTARO YAMAMOTO [Opens in a new window]
TOMMASO MORASCHINI
Affiliation:
DEPARTAMENT DE FILOSOFIA FACULTAT DE FILOSOFIA UNIVERSITAT DE BARCELONA (UB) CARRER MONTALEGRE 6, 08001 BARCELONA, SPAIN E-mail: tommaso.moraschini@ub.edu
JOHANN J. WANNENBURG
Affiliation:
ÚSTAV INFORMATIKY AKADEMIE VĚD ČESKÉ REPUBLIKY POD VODÁRENSKOU VĚŽÍ 2 182 07 PRAHA 8, THE CZECH REPUBLIC and SCHOOL OF MATHEMATICS UNIVERSITY OF THE WITWATERSRAND JOHANNESBURG, SOUTH AFRICA and DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS UNIVERSITY OF PRETORIA PRIVATE BAG X20, HATFIELD PRETORIA 0028, SOUTH AFRICA E-mail: jamie.wannenburg@up.ac.za
KENTARO YAMAMOTO*
Affiliation:
ÚSTAV INFORMATIKY AKADEMIE VĚD ČESKÉ REPUBLIKY POD VODÁRENSKOU VĚŽÍ 2 182 07 PRAHA 8, THE CZECH REPUBLIC
*
E-mail: yamamoto@cs.cas.cz
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Abstract

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

Keywords

Keisler isomorphism theorempositive model theoryprime productpositively existentially closed modelh-inductive theory

MSC classification

Primary: 03C07: Basic properties of first-order languages and structures 03C10: Quantifier elimination, model completeness and related topics 03C20: Ultraproducts and related constructions

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 90 , Issue 3 , September 2025 , pp. 1129 - 1146
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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