3 papers
math.LO2026
More on expressibility of satisfiability in submodels and extensions
Nikolai L. Poliakov, Denis I. Saveliev
We study expressibility in infinitary languages of the modal operators associated with satisfiability of sentences of these languages in submodels and extensions of models. We give…
math.GN2025
On embedding of partially ordered sets in
Nikolai L. Poliakov, Denis I. Saveliev
A natural question, which appeared as Problem 61 in Hart and van Mill's list of open problems on (2024), asks whether every finite partial order is embeddable in the Rudin--…
math.GN2024
Hindman's finite sums theorem and its application to topologizations of algebras
Denis I. Saveliev
The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving th…