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The theory of successor with an extra predicate. (English) Zbl 0369.02025


MSC:

03B25 Decidability of theories and sets of sentences
03C35 Categoricity and completeness of theories
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References:

[1] Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proc. Int. Congr. Logic, Method. and Philos. Sci. 1960, 1-11. Stanford University Press 1962
[2] Büchi, J.R., Landweber, L.H.: Definability in the monadic second-order theory of successor. J. Symb. Logic34, 166-170 (1969) · Zbl 0209.02203
[3] Elgot, C.C., Rabin, M.O.: Decidability and undecidability of extensions of second (first) order theories of (generalized) successor. J. Symb. Logic31, 169-181 (1966) · Zbl 0144.24501
[4] Flum, J.: First order logic and its extensions. In: Logic Conference Kiel 1974, 248-310. Lecture Notes in Mathematics 499. Berlin, Heidelberg, New York: Springer 1975
[5] Hanf, W.P.: Model-theoretic methods in the study of elementary logic. In: The theory of models, 132-145. Amsterdam: North-Holland 1965 · Zbl 0166.25801
[6] Rogers, H., Jr.: Theory of recursive functions and effective computability. New York: McGraw-Hill 1967 · Zbl 0183.01401
[7] Siefkes, D.: Decidable extensions of monadic second order successor arithmetic. In: Automatentheorie und formale Sprachen, 441-472. Mannheim: Bibliogr. Inst. 1969
[8] Siefkes, D.: Undecidable extensions of monadic second order successor arithmetic. Z. f. Math. Logik und Grundlagen d. Math.17, 385-394 (1971) · Zbl 0225.02032
[9] Thomas, W.: Das Entscheidungsproblem für einige Erweiterungen der Nachfolger-Arithmetik. Dissertation. Universität Freiburg 1975
[10] Thomas, W.: A note on undecidable extensions of monadic second order successor arithmetic. Arch. math. Logik17, 43-44 (1975) · Zbl 0325.02032
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