References
Büchi, J.R.: On a decision method in restricted second-order arithmetic. In: Logic Meth. Phil. Sc., Proc. 1960 Stanford Inter. Congr. Stanford 1962, 1–11.
Büchi, J.R., Landweber, L.H.: Definability in the monadic second-order theory of successor. J. Symb. Logic34 (1969), 166–170.
Büchi, J.R., Siefkes, D.: Decidable theories II: The monadic second order theory of all countable ordinals. Lect. Notes Math. 328. Springer-Verlag, Berlin-Heidelberg-New York 1973.
Hanf, W.: Model theoretic methods in the study of elementary logic. In: The theory of models, Proc. 1963 Int. Symp. Berkeley (Ed. Addison, Henkin, Tarski). Amsterdam 1965, 132–145.
McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Information and Control9 (1966), 521–530.
Myhill, J.: Creative sets. Z. Math. Logik Grundl. Math.1 (1955), 97–108.
Rabin, M.O.: A simple method for undecidability proofs and some applications. In: Logic Meth. Phil. Sc., Proc. 1964 Jerusalem Inter. Congr. Amsterdam 1965, 58–68.
Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Transactions AMS141 (1969), 1–35.
Rabin, M.O.: Automata on infinite objects and Church's problem. Conference Board Math. Sc., Regional Conf. Series in Math., No. 13, AMS, Providence, 1972.
Robinson, J.: Definability and decision problems in arithmetic. J. Symb. Logic14 (1949), 98–114.
Robinson, R.M.: Restricted set-theoretical definitions in arithmetic. Proc. AMS9, (1958), 238–242.
Siefkes, D.: Decidable monadic second order theories of arithmetic. Ph.D. thesis Heidelberg 1969.
Siefkes, D.: Decidable theories I: Büchi's monadic second order successor arithmetic. Lect. Notes Math. 120, Springer-Verlag, Berlin-Heidelberg-New York 1970.
Specker, E.: Eine Verschärfung des Unvollständigkeitssatzes des Zahlentheorie. Bull. Acad. Pol. Sci., Cl. III, Vol.5 (1957), 1041–1045.
Tarski, A., Mostowski, A., Robinson, R.M.: Undecidable theories. Amsterdam 1953.
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Siefkes, D. The recursive sets in certain monadic second order fragments of arithmetic. Arch math Logik 17, 71–80 (1975). https://doi.org/10.1007/BF02280817
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DOI: https://doi.org/10.1007/BF02280817