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The Monadic Theory of ω 1 2
Journal of Symbolic Logic 48 (2):387-398 (1983)
Abstract
Assume ZFC + "There is a weakly compact cardinal" is consistent. Then: For every $S \subseteq \omega, \mathrm{ZFC} +$ "S and the monadic theory of ω 2 are recursive each in the other" is consistent; and ZFC + "The full second-order theory of ω 2 is interpretable in the monadic theory of ω 2 " is consistent.Links
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Citations of this work
The structure of the models of decidable monadic theories of graphs.D. Seese - 1991 - Annals of Pure and Applied Logic 53 (2):169-195.
The expressive power of Malitz quantifiers for linear orderings.Hans-Peter Tuschik - 1987 - Annals of Pure and Applied Logic 36:53-103.
The monadic theory of (ω 2, <) may be complicated.Shmuel Lifsches & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):207-213.
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