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Omitting types and AF algebras

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Abstract

We prove that the classes of UHF algebras and AF algebras, while not axiomatizable, can be characterized as those C*-algebras that omit certain types in the logic of metric structures.

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Author information

Author notes

  1. Kevin Carlson

    Present address: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK

  2. Enoch Cheung

    Present address: Department of Mathematical Sciences, Carnegie Mellon University, Wean Hall 6113, Pittsburgh, PA, 15213, USA

  3. Nigel Sequeira

    Present address: Institute for Logic, Language, and Computation, Universiteit van Amsterdam, 1090, Amsterdam, GE, The Netherlands

Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47408, USA

    Kevin Carlson

  2. Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, CA, 94720, USA

    Enoch Cheung

  3. Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, ON, M3J 1P3, Canada

    Ilijas Farah

  4. Matematicki Institut, Kneza Mihaila 35, Belgrade, Serbia

    Ilijas Farah

  5. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Alexander Gerhardt-Bourke

  6. Department of Mathematics and Statistics, McMaster University, 1280 Main Street, West Hamilton, ON, L8S 4K1, Canada

    Bradd Hart & Nigel Sequeira

  7. Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, ON, N1G 2W1, Canada

    Leanne Mezuman

  8. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    Alexander Sherman

Authors
  1. Kevin Carlson
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  2. Enoch Cheung
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  3. Ilijas Farah
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  4. Alexander Gerhardt-Bourke
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  5. Bradd Hart
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  6. Leanne Mezuman
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  7. Nigel Sequeira
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  8. Alexander Sherman
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Corresponding author

Correspondence to Ilijas Farah.

Additional information

This research was supported by the Fields–MITACS undergraduate summer research program in July and August 2012.

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Carlson, K., Cheung, E., Farah, I. et al. Omitting types and AF algebras. Arch. Math. Logic 53, 157–169 (2014). https://doi.org/10.1007/s00153-013-0360-9

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