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Construction of nice trees

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 619)

Abstract

We construct a recursive class of trees having decidable theories in Lo(Q1). Furthermore this class is a dense class of trees. The methods which we use are similar to those of H. Läuchli and J.Leonhard [4]. From our construction the decidability of TR(X 1), the theory of uncountable trees in Lo(Q1), follows as a corollary. This was first proved by H.Herre

Keywords

  • Winning Strategy
  • Order Language
  • Local Game
  • Extended Term
  • Partial Isomorphism

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.

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References

  1. A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961), 129–141

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  2. H. Herre, Entscheidungsprobleme für Theorien in Logikem mit verallgemeinerten Quantoren, Dissertation B, Berlin 1976

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  3. H.J. Keisler, Logic with the quantifier "there exist uncountably many", Ann. Math.Logic 1, (1970), 1–93

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  4. H. Läuchli & J. Leonhard, On the elementary theory of linear order, Fund. Math. LIX (1966)

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  5. L.D. Lipner, Some aspects of generalized quantifiers, Thesis, The University of California at Berkley, (1970)

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  6. A. Mostowski, On a generalization of quantifiers, Fund. Math., vol. 44 (1957), 12–36

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  7. S. Vinner, A generalization of Ehrenfeucht's game and some applications, Israel Journal of Math., vol. 12 No 3, (1972)

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© 1977 Springer-Verlag

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Seese, D.G., Tuschik, H.P. (1977). Construction of nice trees. In: Lachlan, A., Srebrny, M., Zarach, A. (eds) Set Theory and Hierarchy Theory V. Lecture Notes in Mathematics, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067657

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  • DOI: https://doi.org/10.1007/BFb0067657

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08521-8

  • Online ISBN: 978-3-540-37032-1

  • eBook Packages: Springer Book Archive