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
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References
A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961), 129–141
H. Herre, Entscheidungsprobleme für Theorien in Logikem mit verallgemeinerten Quantoren, Dissertation B, Berlin 1976
H.J. Keisler, Logic with the quantifier "there exist uncountably many", Ann. Math.Logic 1, (1970), 1–93
H. Läuchli & J. Leonhard, On the elementary theory of linear order, Fund. Math. LIX (1966)
L.D. Lipner, Some aspects of generalized quantifiers, Thesis, The University of California at Berkley, (1970)
A. Mostowski, On a generalization of quantifiers, Fund. Math., vol. 44 (1957), 12–36
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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