Iterations of Boolean algebras with measure
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 \(Cov(L_{\kappa})\).
scientific article; zbMATH DE number 4125396
scientific article