Parametrized Measuring and Club Guessing

David Aspero, John Krueger

Research output: Contribution to journalArticle

Abstract

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 omega1 is measured by some club subset of omega1. The consistency of Strong Measuring with the negation of CH is shown, solving an open problem from [Aspero and Mota, Few new reals] about parametrized measuring principles. Specifically, we prove that Strong Measuring follows from MRP together with Martin's Axiom for \sigma-centered forcings, as well as from BPFA. Also, Strong Measuring is shown to be consistent with the continuum being arbitrarily large.
Original languageEnglish
Number of pages20
JournalJournal of Mathematical Logic (jml)
Publication statusSubmitted - 20 Oct 2018

Cite this