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math.LO2026
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…
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.LO2018
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…