Rado’s Conjecture is a compactness/reflection principle that says any nonspecial tree of height [Formula: see text] has a nonspecial subtree of size [Formula: see text]. Though incompatible with Martin’s Axiom, Rado’s Conjecture turns out to have many interesting consequences that are also implied by certain forcing axioms. In this paper, we obtain consistency results concerning Rado’s Conjecture and its Baire version. In particular, we show that a fragment of [Formula: see text], which is the forcing axiom for Baire Indestructibly Proper forcings, is compatible with the Baire Rado’s Conjecture. As a corollary, the Baire Rado’s Conjecture does not imply Rado’s Conjecture. Then we discuss the strength and limitations of the Baire Rado’s Conjecture regarding its interaction with stationary reflection principles and some families of weak square principles. Finally, we investigate the influence of Rado’s Conjecture on some polarized partition relations.

中文翻译：

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拉多猜想及其贝尔版本

拉多猜想是一个紧致/反射原理，它说任何高度的非特殊树 [公式：参见文本] 都有一个大小为 [公式：参见文本] 的非特殊子树。尽管与马丁公理不相容，但拉多猜想却产生了许多有趣的结果，这些结果也被某些强迫公理所暗示。在本文中，我们获得了关于 Rado 猜想及其贝尔版本的一致性结果。特别是，我们证明了 [公式：见文本] 的一个片段，它是 Baire Indestructively Pro 强迫的强迫公理，与 Baire Rado 猜想兼容。作为推论，Baire Rado 猜想并不意味着 Rado 猜想。然后我们讨论了贝尔拉多猜想与静止反射原理和一些弱平方原理族相互作用的优势和局限性。最后，我们研究了拉多猜想对一些极化分配关系的影响。