The Monadic Theory of $\omega^1_2$
Gurevich, Yuri ; Magidor, Menachem ; Shelah, Saharon
J. Symbolic Logic, Tome 48 (1983) no. 1, p. 387-398 / Harvested from Project Euclid
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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.
Publié le : 1983-06-14
Classification:  
@article{1183741255,
     author = {Gurevich, Yuri and Magidor, Menachem and Shelah, Saharon},
     title = {The Monadic Theory of $\omega^1\_2$},
     journal = {J. Symbolic Logic},
     volume = {48},
     number = {1},
     year = {1983},
     pages = { 387-398},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741255}
}

Gurevich, Yuri; Magidor, Menachem; Shelah, Saharon. The Monadic Theory of $\omega^1_2$. J. Symbolic Logic, Tome 48 (1983) no. 1, pp.  387-398. http://gdmltest.u-ga.fr/item/1183741255/