Arities and aritizabilities of first-order theories
Sergey V. Sudoplatov
TL;DR
This paper explores the possible arities of elementary theories and their expansions, examining their relationships with Boolean algebras, disjoint unions, and structure compositions, and describing the dynamics of arities.
Contribution
It introduces a comprehensive analysis of arities and aritizabilities of first-order theories, including their connections to various algebraic and structural operations.
Findings
Identifies links between arities and Boolean algebras
Describes how arities relate to disjoint unions and compositions
Analyzes the dynamics of arities in theories
Abstract
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of theories is described.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation · Advanced Topics in Algebra