Published online by Cambridge University Press: 12 March 2014
Assume ZFC + “There is a weakly compact cardinal” is consistent. Then:
(i) For every S ⊆ ω, ZFC + “S and the monadic theory of ω2 are recursive each in the other” is consistent; and
(ii) ZFC + “The full second-order theory of ω2 is interpretable in the monadic theory of ω2” is consistent.
The results were obtained and the paper was written during the Logic Year in the Institute for Advanced Studies of Hebrew University.
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