4 papers
On skew ultralimits and their applications in ultrafilter theory
Nikolai L. Poliakov
We define a special version of the ultralimit, called the skewed ultralimit. Using this tool, we show that the set of ultrafilter types in the -equivalence class of a Ramsey ult…
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…
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--Ke…
On ultrafilter extensions of first-order models and ultrafilter interpretations
Nikolai L. Poliakov, Denis I. Saveliev
There exist two known canonical types of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra o…