TL;DR
This paper explores the relationships between first-order formulas and properties across theories and structures, detailing ranks, degrees, and generic characteristics for formulas and theories.
Contribution
It introduces new characterizations of ranks, degrees, and generic properties for formulas and theories within the framework of first-order logic.
Findings
Descriptions of ranks and degrees for formulas and theories.
Characterizations of generic sentences and theories.
Analysis of links between formulas and properties in various classes.
Abstract
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties are described. Characteristics for generic sentences and generic theories with respect to properties are described and characterized.
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Taxonomy
TopicsOptics and Image Analysis · Advanced Algebra and Logic · Computational Drug Discovery Methods