Fragments of Martin's Maximum in generic extensions

Fragments of Martin's Maximum in generic extensions

We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (ω1 + 1)‐game‐closed forcings. PFA can be destroyed by a strongly (ω1 + 1)‐game‐closed forcing but not by an ω2‐closed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical logic quarterly 2004-05, Vol.50 (3), p.297-302
Hauptverfasser: König, Bernhard, Yoshinobu, Yasuo
Format: Artikel
Sprache:eng
Schlagworte:
Banach-Mazur game
forcing axioms
generic extension
Martin's maximum
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (ω1 + 1)‐game‐closed forcings. PFA can be destroyed by a strongly (ω1 + 1)‐game‐closed forcing but not by an ω2‐closed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.200410101