Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
J.R. Büchi, Weak second order arithmetic and finite automata, Z. Math. Logik und Grundl. Math. 6 (1960), 66–92.
_____, On a decision method in restricted second order arithmetic, Proc. 1960 Int. Cong. for Logic, Method and Philos. of Sci., Stanford Univ. Press, Stanford, Calif., 1962.
_____, Decision methods in the theory of ordinals, Bull. Am. Math. Soc. 71 (1965), 767–770.
_____, Transfinite automata recursions and weak second order theory of ordinals, Proc. 1964 Int. Cong. for Logic, Method and Philos. of Sci., North-Holland Publishing Co., Amsterdam, 1965.
Büchi and Landweber, Solving sequential conditions by finite-state strategies, Trans. Am. Math. Soc. 138 (1969), 295–311.
__________, Definability in the monadic second-order theory of successor, Journ. Sym. Logic 34 (1969), 166–170.
A. Church, Logic arithmetic and automata, Proc. Int. Congr. Math 1962, Almquist and Wiksells, Uppsala, 1963.
J. Doner, Tree acceptors and some of their applications, Journ. Computer and System Sci. 4 (1970), 406–451.
A. Ehrenfeucht, Application of games to the completeness problem for formalized theories, Fund. Math. 49 (1960–61), 129–141.
C.C. Elgot, Decision problems of finite automata design and related arithmetics, Trans. Am. Math. Soc. 98 (1961), 21–51.
Feferman and Vaught, The first order properties of products of algebraic systems, Fund. Math. 47 (1959), 57–103.
H. Läuchli, A decision procedure for the weak second order theory of linear order, Contributions to mathematical logic, Proceeding of the Logic Colloquium, Hannover, 1966, North-Holland, Amsterdam, 1968.
R. McNaughton, Testing and generating infinite sequences by a finite automaton, Information and Control 9 (1966), 521–530.
M.O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Am. Math. Soc. 141 (1969), 1–35.
D. Siefkes, Büchi's monadic second order successor arithmetic, Lecture Notes in Mathematics, vol. 120, Springer-Verlag, Berlin, 1970.
Th. Skolem, Untersuchungen über die Axiome des Klassenkalküls und über Produktations-und Summationsprobleme, welche gewisse Klassen von Aussagen betreffen, Skrifter, Videnskabsakademiet i Kristiania, no. 3, 1919.
S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fu. Ma. 16 (1930), 140–150.
L. Löwenheim, Über Möglichkeiten im Relativkalkül, Fund. Math. 76 (1915), 447–470
Editor information
Rights and permissions
Copyright information
© 1973 Springer-Verlag
About this chapter
Cite this chapter
Büchi, J.R. (1973). The monadic second order theory of ω1 . In: Müller, G.H., Siefkes, D. (eds) Decidable Theories II. Lecture Notes in Mathematics, vol 328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082721
Download citation
DOI: https://doi.org/10.1007/BFb0082721
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06345-2
Online ISBN: 978-3-540-46946-9
eBook Packages: Springer Book Archive