Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T00:24:36.307Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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

REFERENCES

[Ba]Baumgartner, James E., A new class of order types, Annals of Mathematical Logic, vol. 9 (1976), pp. 187–222.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. 1–127.CrossRefGoogle Scholar
[FV]Feferman, S. and Vaught, R. L., The first-order properties of products of algebraic systems, Fundamenta Mathematicae vol. 47 (1959), pp. 57–103.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. 379–419.CrossRefGoogle Scholar
[Sh2]Shelah, Saharon, A weak generalization of MA to higher cardinals, Israel Journal of Mathematics, vol. 30 (1978), pp. 297–306.CrossRefGoogle Scholar
[Sho]Shoenfield, J. R., Unramified forcing, Axiomatic set theory, American Mathematical Society, Providence, R. I., 1971, pp. 357–381.CrossRefGoogle Scholar
[St & Ki]Steinhorn, Charles I. and King, James H., The uniformization property for ℵ2, Israel Journal of Mathematics (to appear).Google Scholar