On ultrafilter extensions of first-order models and ultrafilter interpretations

Abstract

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them (Goranko in Filter and ultrafilter extensions of structures: universal-algebraic aspects, preprint, 2007) comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski (

A note on the Canonical Ramsey Theorem and Ramsey ultrafilters

“…Ultrafilter extensions of arbitrary n-ary maps (and, more broadly, of first-order models) have been introduced independently in recent works by Goranko [2] and Saveliev [3,14]. Further studies can be found in [15,16,17,18].…”