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Archive for Mathematical Logic

, Volume 45, Issue 1, pp 97–112 | Cite as

The Chang-Łoś-Suszko theorem in a topological setting

  • Paul Bankston
Article

Abstract.

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

Key words or phrases:

Co-elementary hierarchy Co-existential mapping Ultracopower Ultracoproduct Compactum Continuum Covering dimension Multicoherence degree Chang-Łoś-Suszko theorem 

Mathematics Subject Classification (2000)

Primary 03C20 54B35 54C10 54D30 Secondary 03C52 06D05 54D35 54F15 54F45 54F55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and Computer ScienceMarquette UniversityMilwaukeeUSA

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