ELEMENTARY EQUIVALENCE IN POSITIVE LOGIC VIA PRIME PRODUCTS

被引：0

作者：

Moraschini, Tommaso ^{[1
]}

Wannenburg, Johann J. ^{[2
,3
]}

Yamamoto, Kentaro ^{[2
,4
]}

机构：

[1] Univ Barcelona UB, Dept Filosofia, Fac Filosofia, Carrer Montalegre 6, Barcelona 08001, Spain

[2] Ustav Informatiky Akad Ved Ceske Republiky, Pod Vodarenskou Vezi 2, Prague 8, Czech Republic

[3] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[4] Univ Pretoria, Dept Math & Appl Math, Private Bag X20, ZA-0028 Pretoria, South Africa

来源：

JOURNAL OF SYMBOLIC LOGIC | 2023年

关键词：

Keisler isomorphism theorem; positive model theory; prime product; positively existentially closed model; h-inductive theory;

D O I：

10.1017/jsl.2023.50

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Los'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.

引用

页数：18

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