Ultraproducts and Related Constructions

• Published in: Mathematics (Basel) Vol. 11; no. 1; p. 70
• Main Author: Sági, Gábor
• Format: Journal Article
• Language: English
• 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

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...