Projective forcing (Q1365248)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Projective forcing |
scientific article; zbMATH DE number 1054203
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Projective forcing |
scientific article; zbMATH DE number 1054203 |
Statements
Projective forcing (English)
0 references
7 December 1997
0 references
The authors study Martin's axiom (MA) restricted to all ccc partial orders which have a projective definition, denoted MA(proj). It is shown that, starting from a model of ZFC, MA(proj) can be forced by a finite-support iteration of ccc projective forcings. It is also shown that consistently MA(proj) is strictly weaker than MA. Several arguments for this are given, some of them, but not all, involving the existence of a weakly compact cardinal. E.g. the consistency of MA(proj) with the negation of CH and the existence of a Suslin tree is proved, assuming Con(ZF+ \(\exists \kappa\) weakly compact).
0 references
Martin's axiom
0 references
projective sets
0 references
forcing
0 references
weakly compact cardinal
0 references
ccc partial orders
0 references
0 references
0 references
