Some metalogical properties for infinitary predicate topological logic

TL;DR

This paper establishes key logical properties such as completeness, interpolation, and omitting types for advanced predicate topological logics that extend first-order logic, and counts non-isomorphic models of countable theories.

Contribution

It introduces new results on the properties of infinitary predicate topological logic extending classical first-order logic.

Findings

Proves completeness, interpolation, and omitting types for the logic.

Counts non-isomorphic topological models of a countable theory.

Abstract

We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory