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Undecidable theories in stationary logic


Authors: Detlef Seese, Peter Tuschik and Martin Weese
Journal: Proc. Amer. Math. Soc. 84 (1982), 563-567
MSC: Primary 03C80; Secondary 03D35
DOI: https://doi.org/10.1090/S0002-9939-1982-0643750-3
MathSciNet review: 643750
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Abstract: It is shown that the theories of the following classes become undecidable in stationary logic: Well orderings with one unary predicate, linear orderings, and Boolean algebras. This is done by interpreting the theory of symmetric reflexive graphs.


References [Enhancements On Off] (What's this?)

  • [1] J. Barwise, M. Kaufmann and M. Makkai, Stationary logic, Ann. Math. Logic 13 (1978), 171-224. MR 486629 (82f:03031a)
  • [2] A. Baudisch, D. Seese, H.-P. Tuschik and M. Weese, Decidability and generalized quantifiers, Akademie-Verlag, Berlin, 1980. MR 588326 (82i:03048)
  • [3] J. R. Büchi, The monadic second order theory of $ {\omega _1} $, Lecture Notes in Math., vol. 328, Springer, Berlin and New York, 1973, pp. 1-127. MR 0476471 (57:16033)
  • [4] P. Eklof and A. Mekler, Stationary logic of finitely determined structures, Ann. Math. Logic 17 (1980), 227-269. MR 556893 (82f:03033)
  • [5] J. Hutchinson, Order types of ordinals in models of set theory, J. Symbolic Logic 41 (1976), 489-502. MR 0403958 (53:7767)
  • [6] K. Kunen, Combinatorics, in Handbook of Mathematical Logic (J. Barwise, editor), North-Holland, Amsterdam, 1977. MR 0457132 (56:15351)
  • [7] D. Seese, Stationary logic and ordinals. Trans. Amer. Math. Soc. 263 (1981), 111-124. MR 590414 (82f:03034)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0643750-3
Keywords: Stationary logic, undecidability, linear ordering, Boolean algebra
Article copyright: © Copyright 1982 American Mathematical Society

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