Describing groups using first-order language
Yuki Maehara
TL;DR
This paper explores how infinite and finite groups can be described using first-order logic, focusing on axiomatizability and compressibility to understand their logical complexity.
Contribution
It introduces and analyzes the concepts of quasi-finite axiomatizability and polylogarithmic compressibility for groups in first-order language.
Findings
Infinite groups' axiomatizability properties examined
Finite groups' description complexity analyzed
New notions of logical compressibility proposed
Abstract
We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.
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Taxonomy
TopicsFinite Group Theory Research · Rings, Modules, and Algebras · Advanced Algebra and Logic