Affiliation:
1. RWTH Aachen University, Germany
Abstract
The decidability of the weak monadic theory of successor is usually considered as a consequence of the connection between monadic second-order logic and finite automata, as established around 1960 in papers of Büchi, Elgot, and Trakhtenbrot. However, there are several remarks and footnotes in papers of that time indicating that the result is also derivable from a theorem of A. Ehrenfeucht using an unpublished remark of R. L. Vaught. In the present note we review these hints and provide a proof along these lines. This simple argument is of methodological interest since it relies solely on first-order model theory and does not use finite automata.
Publisher
Association for Computing Machinery (ACM)
Reference13 articles.
1. Elgot, Decision problems of weak second order arithmetics and finite automata, Preliminary Report;Büchi J. R.;Part I. Notices Amer. Math. Soc.,1958
2. Weak Second-Order Arithmetic and Finite Automata
3. Decision methods in the theory of ordinals
4. A. Ehrenfeucht Application of games to some problems of mathematical logic Bull. Acad. Polon. Sci. Cl. 3 Vol. 5. (1957) 35--37. A. Ehrenfeucht Application of games to some problems of mathematical logic Bull. Acad. Polon. Sci. Cl. 3 Vol. 5. (1957) 35--37.
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1 articles.
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