Journal of Symbolic Logic

The Monadic Theory of $\omega^1_2$

Yuri Gurevich, Menachem Magidor, and Saharon Shelah

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Abstract

Assume ZFC + "There is a weakly compact cardinal" is consistent. Then: (i) For every $S \subseteq \omega, \mathrm{ZFC} +$ "$S$ and the monadic theory of $\omega_2$ are recursive each in the other" is consistent; and (ii) ZFC + "The full second-order theory of $\omega_2$ is interpretable in the monadic theory of $\omega_2$" is consistent.

Article information

Source
J. Symbolic Logic, Volume 48, Issue 2 (1983), 387-398.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741255

Mathematical Reviews number (MathSciNet)
MR704093

Zentralblatt MATH identifier
0559.03008

JSTOR
links.jstor.org

Citation

Gurevich, Yuri; Magidor, Menachem; Shelah, Saharon. The Monadic Theory of $\omega^1_2$. J. Symbolic Logic 48 (1983), no. 2, 387--398. https://projecteuclid.org/euclid.jsl/1183741255


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