☆ 4.1 Article

On duality and model theory for polyadic spaces

ANNALS OF PURE AND APPLIED LOGIC (2024)

Polyadic sets and homomorphism counting

Luca Reggio

Summary: Lovasz's classical result shows that the isomorphism type of a graph can be determined through homomorphism counts. We present a categorical approach to homomorphism counting using the concept of polyadic (finite) sets, and obtain new results applicable to infinite structures.

ADVANCES IN MATHEMATICS (2022)

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Article Mathematics, Applied

Two applications of topology to model theory

Christopher J. Eagle et al.

Summary: By utilizing the topological concept of pseudocompactness, the article simplifies and enhances a proof concerning Terence Tao's metastability by Caicedo, Duenez, and Iovino. It also establishes the exact relationship between the Omitting Types Theorem and the Baire Category Theorem through the development of a machine that transforms topological spaces into abstract logics.

ANNALS OF PURE AND APPLIED LOGIC (2021)

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Article Mathematics