PFA and precipitousness of the nonstationary ideal

Veličković, Boban

doi:10.1090/proc/13770

PFA and precipitousness of the nonstationary ideal
HTML articles powered by AMS MathViewer

by Boban Veličković PDF

Proc. Amer. Math. Soc. 146 (2018), 791-802 Request permission

Abstract:

We apply Neeman’s method of forcing with side conditions to show that PFA does not imply the precipitousness of the nonstationary ideal on $\omega _1$.

References

Matthew Foreman, Ideals and generic elementary embeddings, Handbook of set theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 885–1147. MR 2768692, DOI 10.1007/978-1-4020-5764-9_{1}4
M. Foreman, M. Magidor, and S. Shelah, Martin’s maximum, saturated ideals, and nonregular ultrafilters. I, Ann. of Math. (2) 127 (1988), no. 1, 1–47. MR 924672, DOI 10.2307/1971415
Fred Galvin and András Hajnal, Inequalities for cardinal powers, Ann. of Math. (2) 101 (1975), 491–498. MR 376359, DOI 10.2307/1970936
F. Galvin, T. Jech, and M. Magidor, An ideal game, J. Symbolic Logic 43 (1978), no. 2, 284–292. MR 485391, DOI 10.2307/2272827
T. Jech, M. Magidor, W. Mitchell, and K. Prikry, Precipitous ideals, J. Symbolic Logic 45 (1980), no. 1, 1–8. MR 560220, DOI 10.2307/2273349
Richard Laver, Precipitousness in forcing extensions, Israel J. Math. 48 (1984), no. 2-3, 97–108. MR 770692, DOI 10.1007/BF02761155
Itay Neeman, Forcing with sequences of models of two types, Notre Dame J. Form. Log. 55 (2014), no. 2, 265–298. MR 3201836, DOI 10.1215/00294527-2420666
Saharon Shelah, Proper and improper forcing, 2nd ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998. MR 1623206, DOI 10.1007/978-3-662-12831-2