A logic of co-valuations

Speaker(s)

Maciej Malicki

Affiliation

University of Warsaw

Language of the talk

Polish

Date

Jan. 7, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory - such as ultraproducts, compactness, and omitting types - can be developed in this setup. 
Using a recently discovered duality between certain countable posets and second-countable compact T_1 spaces, we prove that these spaces are counterparts of countable universes in first-order logic. Thus, although no topology appears in the initial formulation, the logic of co-valuations turns out to be naturally suited for studying objects endowed with a compact topology. Standard topological notions, such as connectedness and covering dimension, are easily expressible, and model-theoretic properties, including atomicity, can be effectively analyzed. 
The framework also interacts well with Fraïssé-type constructions.

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