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An algebraic treatment of the barwise compactness theory

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Abstract

A theorem on the extendability of certain subsets of a Boolean algebra to ultrafilters which preserve countably many infinite meets (generalizing Rasiowa-Sikorski) is used to pinpoint the mechanism of the Barwise proof in a way which bypasses the set theoretical elaborations.

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References

  1. J. Barwise, Admissible Sets and Structures. Springer Berlin, 1975.

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  2. C. R. Karp, Languages with Expressions of Infinite Length, North Holland, Amsterdam, 1964.

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  3. H. J. Keisler, Model Theory for Infinitary Logic, North Holland, Amsterdam, 1971.

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  4. H. Rasiowa and R. Sikorski, The Mathematics of Meta-Mathematics, Polish Academy of Sciences, Warszawa, 1963.

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  5. M. Makkai, Admissible sets and infinitary logic, in Handbook of Mathematical Logic, J. Barwise (ed.), North Holland, Amsterdam, 1977.

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Authors and Affiliations

  1. Department of Mathematics, University of Windsor, Canada

    Isidore Fleischer & Philip Scott

  2. Department of Mathematics, University of Ottawa, Canada

    Isidore Fleischer & Philip Scott

Authors
  1. Isidore Fleischer
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  2. Philip Scott
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Additional information

During the preparation of this work the second author was a postdoctoral visitor at the C. R. M. supported by a National Council of Canada operating grant.

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Fleischer, I., Scott, P. An algebraic treatment of the barwise compactness theory. Stud Logica 50, 217–223 (1991). https://doi.org/10.1007/BF00370183

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  • DOI: https://doi.org/10.1007/BF00370183

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