Ultraproducts and Related Constructions

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 secon...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 1; p. 70
Main Author Sági, Gábor
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2023
Subjects
Algebraic topology
Analysis
finite Ramsey theory
first order logic
Geometry
Mathematical research
Ramsey theory
second order logic
Topology
ultrafilter
ultraproduct
ultraproducts in general topology
Hungary
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11010070