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The monadic theory of ω21

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich ,
Menachem Magidor  and
Saharon Shelah
Yuri Gurevich
Affiliation:
Ben-Gurion University, Beer-Sheva, Israel
Menachem Magidor
Affiliation:
University of Michigan, Ann Arbor, Michigan 48109
Saharon Shelah
Affiliation:
Hebrew University, Jerusalem, Israel
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Abstract

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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 2 , June 1983 , pp. 387 - 398
Copyright
Copyright © Association for Symbolic Logic 1983

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Footnotes

1

The results were obtained and the paper was written during the Logic Year in the Institute for Advanced Studies of Hebrew University.

References

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