$\alpha $-Properness and Axiom A

Volume 186 / 2005

Tetsuya Ishiu Fundamenta Mathematicae 186 (2005), 25-37 MSC: Primary 03E40; Secondary 03E35. DOI: 10.4064/fm186-1-2


We show that under ZFC, for every indecomposable ordinal $\alpha<\omega_1$, there exists a poset which is $\beta$-proper for every $\beta<\alpha$ but not $\alpha$-proper. It is also shown that a poset is forcing equivalent to a poset satisfying Axiom A if and only if it is $\alpha$-proper for every $\alpha<\omega_1$.


  • Tetsuya IshiuDepartment of Mathematics
    University of Kansas
    405 Snow Hall, 1460 Jayhawk Blvd.
    Lawrence, KS 66045, U.S.A.

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