Geodesic
$\alpha $-Properness and Axiom A
Tetsuya Ishiu1
1 Department of Mathematics University of Kansas 405 Snow Hall, 1460 Jayhawk Blvd. Lawrence, KS 66045, U.S.A.
Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 25-37.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\alpha\omega_1$.
DOI : 10.4064/fm186-1-2
Keywords: under zfc every indecomposable ordinal alpha omega there exists poset which beta proper every beta alpha alpha proper shown poset forcing equivalent poset satisfying axiom only alpha proper every alpha omega

Tetsuya Ishiu 1

1 Department of Mathematics University of Kansas 405 Snow Hall, 1460 Jayhawk Blvd. Lawrence, KS 66045, U.S.A. 
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Tetsuya Ishiu. $\alpha $-Properness and Axiom A. Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 25-37. doi : 10.4064/fm186-1-2. http://geodesic.mathdoc.fr/articles/10.4064/fm186-1-2/

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