Parametrized Measuring and Club Guessing
Tom 249 / 2020
Fundamenta Mathematicae 249 (2020), 169-183
MSC: Primary 03E05, 03E35; Secondary 03E57.
DOI: 10.4064/fm781-9-2019
Opublikowany online: 13 December 2019
Streszczenie
We introduce Strong Measuring, a maximal strengthening of J. T. Moore’s Measuring principle, which asserts that every collection of fewer than continuum many closed bounded subsets of is measured by some club subset of \omega _1. The consistency of Strong Measuring with the negation of \mathsf {CH} is shown, solving an open problem from Asperó and Mota’s 2017 preprint on Measuring. Specifically, we prove that Strong Measuring follows from \mathsf {MRP} together with Martin’s Axiom for \sigma -centered forcings, as well as from \mathsf {BPFA}. We also consider strong versions of Measuring in the absence of the Axiom of Choice.
