α-Properness and Axiom A

Tetsuya Ishiu¹
Fund. Math. 186 (2005), 25-37
doi:10.4064/fm186-1-2

Abstract: 
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 $\alpha<\omega_1$.

MSC (2000): Primary 03E40; Secondary 03E35.
Retrieve article in PDF (248.78 Kb)

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