Skip to main content Accesibility Help
×
×
Home

Characterising subsets of ω1 constructible from a real

  • P. D. Welch (a1)
Abstract

A small large cardinal upper bound in V for proving when certain subsets of ω1 (including the universally Baire subsets) are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that ∀B ⊆ ω1 [B is universally Baire ⇔ B ϵ L[r] for some real r] is preserved under set-sized forcing extensions if and only if there are arbitrarily large “admissibly measurable” cardinals.

Copyright
References
Hide All
[BG]Baumgartner, J. and Galvin, F., Generalized Erdős cardinals and 0#, Annals of Mathematical Logic, vol. 15 (1978), pp. 289313.
[BJW]Beller, A., Jensen, R. B., and Welch, P. D., Coding the universe, London Mathematical Society Lecture Note Series, no. 47, Cambridge University Press, Cambridge, 1982.
[CM]Dodd, A. J., The core model, London Mathematical Society Lecture Note Series, no. 61, Cambridge University Press, Cambridge, 1982.
[DL]Donder, H.-D. and Levinski, J.-P., Some principles related to Chang's conjecture, Annals of Pure and Applied Logic, vol. 45 (1989), pp. 39101.
[FMW]Feng, Q., Magidor, M., and Woodin, H., Universally Baire sets of reals, Set theory of the continuum (Judah, H.et al., editors), MSRI Publications, no. 26, Springer-Verlag, Berlin, 1992, pp. 203242.
[K1]Kechris, A. S., Subsets of ℵ1 constructible from a real, Cabal seminar 81–85 (Kechris, A.et al., editors), Lecture Notes in Mathematics, vol. 1333, Springer-Verlag, Berlin, 1987, pp. 110116.
[K2]Kechris, A. S., Homogeneous trees and projective scales, Cabal seminar 77–79 (Kechris, A. S.et al., editors), Lecture Notes in Mathematics, vol. 839, Springer-Verlag, Berlin, 1981, pp. 3374.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed