For a canonical model of set theory whose projective theory of the real numbers is stable under set forcing extensions, a set of reals of minimal complexity is constructed which fails to be universally Baire. The construction uses a general method for generating non-universally Baire sets via the Levy collapse of a cardinal, as well as core model techniques. Along the way it is shown (extending previous results of Steel) how sufficiently iterable fine structure models recognize themselves as global core models.
Publié le : 1999-12-14
Classification:
Set Theory,
Descriptive Set Theory,
Inner Models,
Universally Baire Sets,
03E15,
03E45,
54H05,
28A05,
03E55,
03E60
@article{1183745942,
author = {Hauser, Kai},
title = {A Minimal Counterexample to Universal Baireness},
journal = {J. Symbolic Logic},
volume = {64},
number = {1},
year = {1999},
pages = { 1601-1627},
language = {en},
url = {http://dml.mathdoc.fr/item/1183745942}
}
Hauser, Kai. A Minimal Counterexample to Universal Baireness. J. Symbolic Logic, Tome 64 (1999) no. 1, pp. 1601-1627. http://gdmltest.u-ga.fr/item/1183745942/