Iterations of Boolean algebras with measure
type: Item
instance of: scholarly article
title: Iterations of Boolean algebras with measure
zbMATH Open document ID: 0687.03032
DOI: 10.1007/BF01630808
author: Anastasis Kamburelis
published in: Archive for Mathematical Logic
publication date: 1989-01-01T00:00:00Z
review text: The author considers a class M of Boolean algebras with strictly positive, finitely additive measures. He shows that M is closed under iteration with finite support and that forcing via such algebras allows an extension of the Lebesgue measure structure of the ground model. For a class \(\Gamma\) of Boolean algebras let MA(\(\Gamma)\) denote Martin's axiom restricted to \(\Gamma\). B is said to be \(\sigma\)-centered if the Stone space of B is separable. The main result of this paper is: MA(M)\(\equiv MA(\sigma\)-centered) and LC, where LC is the statement that for an infinite cardinal \(\kappa\), \(Cov(L_{\kappa})=2^{\omega}\), with a suitable definition of \(Cov(L_{\kappa})\).
Mathematics Subject Classification ID: 03E40
Mathematics Subject Classification ID: 03E50
Mathematics Subject Classification ID: 28A60
zbMATH DE Number: 4125396
zbMATH Keywords: measures on Boolea algebras
zbMATH Keywords: forcing
zbMATH Keywords: Martin's axiom
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4125396