Skip to main content Accessibility help
×
Home

Bounded Martin's Maximum, weak Erdӧs cardinals, and ψAc

  • David Asperó (a1) and Philip D. Welch (a2)

Abstract

We prove that a form of the Erdӧs property (consistent with V = L[Hω2] and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle ψAC holds, and therefore . We also prove that ψAC implies that every function f: ω1 → ω1 is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum fails.

Copyright

References

Hide All
[Al]Asperó, David, Boundedforcing axioms and the continuum, Ph.D. thesis, University of Barcelona, 2000.
[A2]Asperó, David, Bounded forcing axioms and the size of the continuum, submitted.
[A-B]Asperó, David and Bagaria, Joan, Bounded forcing axioms and the continuum, Annals of Pure and Applied Logic, vol. 109 (2001), pp. 179203.
[B]Bagaria, Joan, Bounded forcing axioms as principles of generic absoluteness, Archive for Mathematical Logic, vol. 39 (2000), pp. 393401.
[Ba-G]Baumgartner, James and Galvin, Fred, Generalized Erdӧs cardinals and 0#, Annals of Mathematical Logic, vol. 15 (1978), pp. 289313.
[D-Do]Deiser, Oliver and Donder, Hans-Dieter, Canonical Functions, non-regular ultrafilters and Ulam's problem on ω1, submitted.
[Do-K]Donder, Hans-Dieter and Koepke, Peter, On the consistency strength of ‘accessible’ Jo´nsson cardinals, Annals of Mathematical Logic, vol. 25 (1983), pp. 233261.
[Do-L]Donder, Hans-Dieter and Levinski, Jean-Pierre, Some principles related to Chang's Conjecture, Annals of Pure and Applied Logic, vol. 45 (1989), pp. 39101.
[F-J]Feng, Qi and Jech, Thomas, Projective stationary sets and strong reflection principles, The Journal of the London Mathematical Society, vol. 58 (1998), pp. 271283.
[Fo-M-S]Foreman, Matthew, Magidor, Menachem, and Shelah, Saharon, Martin's Maximum, saturated ideals, and non–regular ultrafilters. Part I, Annals of Mathematics, vol. 127 (1988), pp. 147.
[G-S]Goldstern, Martin and Shelah, Saharon, The bounded proper forcing axiom, this Journal, vol. 60 (1995), pp. 5873.
[J]Jech, Thomas, Set theory. Second corrected edition, Perspectives in mathematical logic, Springer, Berlin-Heidelberg-New York, 1997.
[Mi]Miyamoto, Tadatoshi, A note on a weak segment of PFA, Proceedings of the sixth asian logic conference (Beijing, 1996) (River Edge, NJ), World Sci. Publishing, 1998, pp. 175197.
[S]Shelah, Saharon, Semiproperforcing axiom implies Martin maximum but not PFA+, this Journal, vol. 52 (1987), pp. 360367.
[W]Welch, Philip, On unfoldable cardinals, ω-closed cardinals, and the beginning of the inner model hierarchy, submitted.
[Wo]Woodin, Hugh, The axiom of determinacy, forcing axioms, and the nonstationary ideal, Series in logic and its applications, number 1, De Gruyter, Berlin, New York, 1999.

Keywords

Related content

Powered by UNSILO

Bounded Martin's Maximum, weak Erdӧs cardinals, and ψAc

  • David Asperó (a1) and Philip D. Welch (a2)

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.