Projective forcing
type: Item
instance of: scholarly article
title: Projective forcing
zbMATH Open document ID: 0878.03037
DOI: 10.1016/S0168-0072(96)00035-8
author: Joan Bagaria
author: Roger Bosch
published in: Annals of Pure and Applied Logic
publication date: 1997-12-07T00:00:00Z
review text: 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).
reviewed by: Otmar Spinas
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 1054203
zbMATH Keywords: Martin's axiom
zbMATH Keywords: projective sets
zbMATH Keywords: forcing
zbMATH Keywords: weakly compact cardinal
zbMATH Keywords: ccc partial orders
MaRDI profile type: Publication
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full work available at URL: s0168-0072(96)00035-8
OpenAlex ID: W4212773510
description: scientific article; zbMATH DE number 1054203