Ultraproducts and Related Constructions

Gábor Sági ()
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Gábor Sági: Alfréd Rényi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary

Mathematics, 2022, vol. 11, issue 1, 1-19

Abstract: In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and second-order existential logics, finite Ramsey theory and general topology. Special emphasis has been made for producing a uniform treatment and for highlighting interconnections between these different subjects.

Keywords: ultrafilter; ultraproduct; first order logic; second order logic; finite Ramsey theory; ultraproducts in general topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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