The measuring principle and the continuum hypothesis

TL;DR

This paper demonstrates that the Measuring principle can be forced without adding new reals and remains consistent with a large continuum, addressing two significant questions in set theory.

Contribution

It proves the consistency of the Measuring principle with a large continuum without adding new reals, answering two open questions by Justin Moore.

Findings

Measuring principle can be forced without adding reals.

Measuring principle is consistent with a large continuum.

Addresses two open questions in set theory.

Abstract

We show that one can force the Measuring principle without adding any new reals. We also show that it is consistent with the large continuum. These results answer two famous questions of Justin Moore.