Some Applications of the Ultrapower Theorem to the Theory of Compacta

Paul Bankston ()
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Paul Bankston: Marquette University, Department of Mathematics, Statistics and Computer Science

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 45-66 from Springer

Abstract: Abstract The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.

Keywords: ultraproduct; ultracoproduct; compactum; continuum; co-elementary map; co-existential map.; 03C20; 54B35; 54C10; 54D05; 54D30; 54D80; 54F15; 54D45; 54F55 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_4

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DOI: 10.1007/978-94-017-2529-3_4

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