Playing with Mathias

摘要

We present a series of axioms that describe the combinatorial core of the Mathias model (countable support iteration of omega(2) Mathias reals over the Continuum Hypothesis). Our axioms are formulated in terms of games with Borel sets and functions and are strong enough to imply most of the propositions usually proved by means of the iterated Mathias forcing. (C) 2020 Elsevier B.V. All rights reserved.