Name
Abstract | ||
|---|---|---|
We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (ω2,ω2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level ω2, and therefore with the existence of an ω2-Suslin tree. We also show that the axiom we call BMMℵ3 implies ℵ2ℵ1=ℵ2, as well as a stationary reflection principle which has many of the consequences of Martin's Maximum for objects of size ℵ2. Finally, we give an example of a so-called boldface bounded forcing axiom implying 2ℵ0=ℵ2. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1016/S0168-0072(00)00058-0 | Annals of Pure and Applied Logic |
Keywords | Field | DocType |
03E35,03E50,03E05,03E65 | Axiom schema,Axiom of choice,Discrete mathematics,Combinatorics,Zermelo–Fraenkel set theory,Scott's trick,Constructive set theory,Axiom independence,Axiom of extensionality,Proper forcing axiom,Mathematics | Journal |
Volume | Issue | ISSN |
109 | 3 | 0168-0072 |
Citations | PageRank | References |
2 | 0.40 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Asperó | 1 | 17 | 6.71 |
| Joan Bagaria | 2 | 63 | 13.15 |