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.
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页数：18
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