Rado's Conjecture and its Baire version

Jing Zhang

Research output: Contribution to journalArticlepeer-review


Rado's Conjecture is a compactness/reflection principle that says any nonspecial tree of height ω1 has a nonspecial subtree of size 1. 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 PFA, 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.

Original languageEnglish
Article number1950015
JournalJournal of Mathematical Logic
Issue number1
StatePublished - 1 Apr 2020
Externally publishedYes

Bibliographical note

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© 2020 World Scientific Publishing Company.


  • Baire tree
  • Rado's Conjecture
  • compactness principles
  • forcing


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