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The monadic theory of ω21

Published online by Cambridge University Press:  12 March 2014

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

Abstract

Assume ZFC + “There is a weakly compact cardinal” is consistent. Then:

(i) For every Sω, 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.

Type
Research Article
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

[Ba]Baumgartner, James E., A new class of order types, Annals of Mathematical Logic, vol. 9 (1976), pp. 187222.CrossRefGoogle Scholar
[Bu]Büchi, J. Richard, The monadic second-order theory of ω 1, Decidable theories. II (Büchi, -Siefkes, , Editors), Lecture Notes in Mathematics, vol. 328, Springer-Verlag, Berlin and New York, 1973, pp. 1127.CrossRefGoogle Scholar
[FV]Feferman, S. and Vaught, R. L., The first-order properties of products of algebraic systems, Fundamenta Mathematicae vol. 47 (1959), pp. 57103.CrossRefGoogle Scholar
[Je]Jech, Thomas, Set theory, Academic Press, New York, 1978.Google Scholar
[Ma]Magidor, Menachem, Reflecting stationary sets, this Journal (to appear).Google Scholar
[Sh1]Shelah, Saharon, The monadic theory of order, Annals of Mathematics, vol. 102 (1974), pp. 379419.CrossRefGoogle Scholar
[Sh2]Shelah, Saharon, A weak generalization of MA to higher cardinals, Israel Journal of Mathematics, vol. 30 (1978), pp. 297306.CrossRefGoogle Scholar
[Sho]Shoenfield, J. R., Unramified forcing, Axiomatic set theory, American Mathematical Society, Providence, R. I., 1971, pp. 357381.CrossRefGoogle Scholar
[St & Ki]Steinhorn, Charles I. and King, James H., The uniformization property for ℵ2, Israel Journal of Mathematics (to appear).Google Scholar
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