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.
|Number of pages||20|
|Journal||Journal of Mathematical Logic (jml)|
|Publication status||Submitted - 20 Oct 2018|