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An axiom system for the weak monadic second order theory of two successors. (English) Zbl 0397.03009

##### MSC:
 03B25 Decidability of theories and sets of sentences 03D05 Automata and formal grammars in connection with logical questions
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##### References:
 [1] J. R. Buchi;Weak second order arithmetic and finite automata, Z. Math. Logik Grundlagen Math.6 (1960), 66–92. · Zbl 0103.24705 · doi:10.1002/malq.19600060105 [2] J. R. Buchi,On a decision method in restricted second order arithmetic, inLogic Meth. Phil. Sc., Proc. 1960 Stanford Int. Congr., Stanford, 1962, pp. 1–11. [3] J. R. Buchi and D. Siefkes,Axiomatization of the monadic second order theory of $$\omega$$ 1, Lect. Notes Math., vol. 328, Springer-Verlag, Berlin-Heidelberg-New York, 1973, pp. 129–217. [4] J. Doner,Tree acceptors and some of their applications, J. Comput. System Sci.4 (1970), 406–451. · Zbl 0212.02901 · doi:10.1016/S0022-0000(70)80041-1 [5] M. Magidor and G. Moran,Finite automata over finite trees, Tech. Rep. No. 30, Dept. Math., The Hebrew University, Jerusalem, 1969. [6] M. O. Rabin,Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc.141 (1969), 1–35. · Zbl 0221.02031 [7] M. O. Rabin,Weakly definable relations and special automata, inMathematical Logic and Foundations of Set Theory, (Y. Bar-Hillel, ed.), Amsterdam, 1970, pp. 1–23. [8] D. Siefkes,Decidable theories I; Buchi’s monadic second order successor artimetic, Lect. Notes Math., Vol. 120, Springer-Verlag, Berlin-Heidelberg-New York, 1970. · Zbl 0213.01901 [9] J. W. Thatcher and J. B. Wright,Generalized finite automata theory with an application to a decision problem of second-order logic, Mat. Systems Theory2 (1968), 57–81. · Zbl 0196.01901 · doi:10.1007/BF01691346
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