Combinations of structures

TL;DR

This paper explores how combining structures with unary predicates and equivalence relations affects properties like $\, ext{ω}$-categoricity and Ehrenfeuchtness, introducing $e$-spectra to analyze these combinations.

Contribution

It characterizes conditions under which structural combinations preserve key logical properties and introduces the concept of $e$-spectra for analyzing these combinations.

Findings

Conditions for preservation of $\, ext{ω}$-categoricity identified

Conditions for preservation of Ehrenfeuchtness characterized

Possible $e$-spectra for combined structures described

Abstract

We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving $\omega$-categoricity and Ehrenfeuchtness under these combinations are characterized. The notions of $e$-spectra are introduced and possibilities for $e$-spectra are described.