Notre Dame Journal of Formal Logic

A Note on Counterexamples to the Vaught Conjecture

Greg Hjorth

Abstract

If some infinitary sentence provides a counterexample to Vaught's Conjecture, then there is an infinitary sentence which also provides a counterexample but has no model of cardinality bigger than ℵ₁.

Article information

Source
Notre Dame J. Formal Logic, Volume 48, Number 1 (2007), 49-51.

Dates
First available in Project Euclid: 1 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1172787544

Digital Object Identifier
doi:10.1305/ndjfl/1172787544

Mathematical Reviews number (MathSciNet)
MR2289896

Zentralblatt MATH identifier
1128.03024

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]

Keywords
Vaught's conjecture infinitary logic Polish group

Citation

Hjorth, Greg. A Note on Counterexamples to the Vaught Conjecture. Notre Dame J. Formal Logic 48 (2007), no. 1, 49--51. doi:10.1305/ndjfl/1172787544. https://projecteuclid.org/euclid.ndjfl/1172787544


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References

  • [1] Becker, H., and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, vol. 232 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1996.
  • [2] Hjorth, G., "Knight's model, its automorphism group, and characterizing the uncountable cardinals", Journal of Mathematical Logic, vol. 2 (2002), pp. 113--44.
  • [3] Lopez-Escobar, E. G. K., "An interpolation theorem for denumerably long formulas", Fundamenta Mathematicae, vol. 57 (1965), pp. 253--72.