Abstract We present a series of axioms that describe the combinatorial core of the Mathias model (countable support iteration of ω 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.

中文翻译：

---

和马蒂亚斯一起玩

摘要 我们提出了一系列公理来描述 Mathias 模型的组合核心（连续统假设上 ω 2 Mathias 实数的可数支持迭代）。我们的公理是根据具有 Borel 集和函数的博弈来制定的，并且足够强大，可以暗示大多数通常通过迭代 Mathias 强迫证明的命题。