Weak square sequences and special Aronszajn trees

Volume 221 / 2013

John Krueger Fundamenta Mathematicae 221 (2013), 267-284 MSC: Primary 03E05. DOI: 10.4064/fm221-3-4


A classical theorem of set theory is the equivalence of the weak square principle $\Box _\mu ^*$ with the existence of a special Aronszajn tree on $\mu ^+$. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general.


  • John KruegerDepartment of Mathematics
    University of North Texas
    1155 Union Circle #311430
    Denton, TX 76203, U.S.A.

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