Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-25T17:09:08.566Z Has data issue: false hasContentIssue false
  • English
  • Français

A co-analytic maximal set of orthogonal measures

Published online by Cambridge University Press:  12 March 2014

Vera Fischer  and
Asger Törnquist
Vera Fischer
Affiliation:
Kurt Gödel Research Center, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria. E-mail: vfischer@logic.univie.ac.at
Asger Törnquist
Affiliation:
Kurt Gödel Research Center, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria. E-mail: asger@logic.univie.ac.at
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that if V = L then there is a maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.

Keywords

Descriptive set theoryconstructible sets
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1403 - 1414
Copyright
Copyright © Association for Symbolic Logic 2010

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.)

References

REFERENCES

[1]Drake, F. R., Set theory, an introduction to large cardinals, North-Holland Publishing Company, 1974.Google Scholar
[2]Gao, S., Invariant descriptive set theory, Taylor and Francis, 2008.CrossRefGoogle Scholar
[3]Gao, S. and Zhang, Y., Definable sets of generators in maximal cofinitary groups. Advances in Mathematics, vol. 217 (2008), no. 2, pp. 814–832.CrossRefGoogle Scholar
[4]Judah, H. and Shelah, S., Δ21-sets of reals, Annals of Pure and Applied Logic, vol. 42 (1989), no. 3, pp. 207–223.Google Scholar
[5]Kakutani, S., On equivalence of infinite product measures, Annals of Mathematics, vol. 49 (1948), pp. 214–224.CrossRefGoogle Scholar
[6]Kanamori, A., The higher infinite, Springer Verlag, 1997.CrossRefGoogle Scholar
[7]Kastermans, B., Cofinitary groups and other almost disjoint families, Ph.D. thesis, University of Michigan, 2006, http://www.beirtk.nl/Files/Papers/thesis.pdf.Google Scholar
[8]Kastermans, B., The complexity of maximal cofinitary groups, Proceedings of the American Mathematical Society, vol. 137 (2009), no. 1, pp. 307–316.CrossRefGoogle Scholar
[9]Kastermans, B., Steprāns, J., and Zhang, Y., Analytic and coanalytic families of almost disjoint functions, this Journal, vol. 73 (2008), no. 4, pp. 1158–1172.Google Scholar
[10]Kechris, A., Measure and category in effective descriptive set theory, Annals of Pure and Applied Logic, vol. 5 (1973), pp. 337–384.Google Scholar
[11]Kechris, A., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, 1995.CrossRefGoogle Scholar
[12]Kechris, A. and Sofronidis, N. E., A strong generic ergodicity property of unitary and self-adjoint operators, Ergodic Theory and Dynamical Systems, vol. 21 (2001), pp. 1459–1479.CrossRefGoogle Scholar
[13]Mansfield, R. and Weitkamp, G., Recursive aspects of descriptive set theory, Oxford University Press, 1985.Google Scholar
[14]Miller, A. W., Infinite combinatorics and definability, Annals of Pure and Applied Logic, vol. 41 (1989), pp. 179–203.CrossRefGoogle Scholar
[15]Moschovakis, Y. N., Descriptive set theory, North-Holland Publishing Co., Amsterdam, 1980.Google Scholar
[16]Preiss, D. and Rataj, J., Maximal sets of orthogonal measures are not analytic, Proceedings of the American Mathematical Society, vol. 93 (1985), pp. 471–476.CrossRefGoogle Scholar