On lambda strongly homogeneity existence for cofinality logics

TL;DR

This paper investigates the existence of lambda-strongly homogeneous models in cofinality logics, demonstrating that certain logics with cofinality quantifiers possess the homogeneous model existence property.

Contribution

It establishes the homogeneous model existence property for cofinality logics with specific classes of regular cardinals, advancing understanding of their model-theoretic properties.

Findings

Cofinality logics with classes of regular cardinals have homogeneous model existence.

The logic L(Q^{cf}_C) exhibits desirable model-theoretic properties.

The paper extends the theory of cofinality logics and their model existence features.

Abstract

Let C subset Reg be a non-empty class (of regular cardinal). Then the logic L(Q^{cf}_C) has additional nice properties: it has homogeneous model existence property.