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Monadic logic: Hanf Numbers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1182)

Abstract

This is part of the classification developed in Baldwin Shelah [BSh]. The paper is divided into two parts. In part I we show that (T , 2nd)≨(T, mon) iff the Hanf number for the theory T in monadic logic is smaller than the Hanf number of second order logic.

For this we deal with partition relations for models of T. The main result is that if T does not have the independence property even after expanding by monadic predicates (or equivalently (T , 2nd)≨(T, mon) then: ℶω+1(λ)+s(λ) T . In Part II we analyze such T getting a decomposition theorem like that in [BSh] (but weaker) (This is needed in part I.)

Keywords

  • Partial Decomposition
  • Stationary Subset
  • Monadic Predicate
  • Indiscernible Sequence
  • Monadic Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

I thank Rami Gromberg for many corrections.

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References

  1. J. Baldwin and S. Shelah. Second order quantifiers and the complexity of theories, Proc. of the 1980/1 model theory year in Jerusalem. Notre Dame J. of Formal Logic, 1985.

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  2. Y. Gurevich and S. Shelah. Monadic Logic and the next world. Proc. of the 1980/1 model theory year in Jerusalem; Israel J. Math, 1985.

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  6. S. Shelah, More on monadic theories, in preparation.

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© 1986 Springer-Verlag

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Shelah, S. (1986). Monadic logic: Hanf Numbers. In: Around Classification Theory of Models. Lecture Notes in Mathematics, vol 1182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098511

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  • DOI: https://doi.org/10.1007/BFb0098511

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16448-7

  • Online ISBN: 978-3-540-39788-5

  • eBook Packages: Springer Book Archive