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Ultraproducts and Related Constructions

Author

Listed:
  • Gábor Sági

    (Alfréd Rényi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary
    Department of Algebra, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary)

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.

Suggested Citation

  • Gábor Sági, 2022. "Ultraproducts and Related Constructions," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:70-:d:1014412
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