LARGE CARDINALS AND DEFINABLE COUNTEREXAMPLES TO THE CONTINUUM-HYPOTHESIS

Authors
FOREMAN M MAGIDOR M
Citation
M. Foreman et M. Magidor, LARGE CARDINALS AND DEFINABLE COUNTEREXAMPLES TO THE CONTINUUM-HYPOTHESIS, Annals of pure and applied Logic, 76(1), 1995, pp. 47-97
Citations number
36
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Annals of pure and applied Logic → ACNP
ISSN journal
01680072
Volume
76
Issue
1
Year of publication
1995
Pages
47 - 97
Database
ISI
SICI code
0168-0072(1995)76:1<47:LCADCT>2.0.ZU;2-N
Abstract
In this paper we consider whether L(R) has ''enough information'' to c ontain a counterexample to the continuum hypothesis. We believe this q uestion provides deep insight into the difficulties surrounding the co ntinuum hypothesis. We show sufficient conditions for L(R) not to cont ain such a counterexample. Along the way we establish many results abo ut nonstationary towers, non-reflecting stationary sets, generalizatio ns of proper and semiproper forcing and Chang's conjecture.