First-order sentences in random groups I: Universal sentences-Reference-Cited by-同舟云学术

First-order sentences in random groups I: Universal sentences

Published:2024-08-15 Issue: Volume: Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Kharlampovich Olga¹,Sklinos Rizos²

Affiliation:

1. Department of Mathematics and Statistics , CUNY Hunter College and Graduate Center , 695 Park Avenue, 10065 , New York , USA

2. Institute of Mathematics , 85320 Academy of Mathematics and Systems Science , 55 Zhongguanchun, 100190 , Beijing , P. R. China

Abstract

Abstract We prove that a random group, in Gromov’s density model with d < 1 / 16

d<1/16

, satisfies a universal sentence 𝜎 (in the language of groups) if and only if 𝜎 is true in a non-abelian free group.

Funder

Simons Foundation

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0055/pdf

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