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Martin’s Maximum and tower forcing

✍ Scribed by Sean Cox, Matteo Viale

Book ID
120953260
Publisher
The Hebrew University Magnes Press
Year
2013
Tongue
English
Weight
391 KB
Volume
197
Category
Article
ISSN
0021-2172

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📜 SIMILAR VOLUMES

Semi-proper forcing, remarkable cardinal
Semi-proper forcing, remarkable cardinals, and Bounded Martin's Maximum
✍ Ralf Schindler 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 150 KB

## Abstract We show that __L__(ℝ) absoluteness for semi‐proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with __L__(ℝ) absoluteness for proper forcings. By [7], __L__(ℝ) absoluteness for stationary set preserving forcings gives an inner model with a st

Martin's Maximum and the Pmaxaxiom(∗)
Martin's Maximum and the Pmaxaxiom(∗)
✍ Paul Larson 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 128 KB

Assuming the existence of a supercompact limit of supercompact cardinals, we modify the original consistency proof of Martin's Maximum to obtain a model in which MM holds but the Pmax axiom ( \* ) fails.

Fragments of Martin's Maximum in generic
Fragments of Martin's Maximum in generic extensions
✍ Bernhard König; Yasuo Yoshinobu 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 137 KB

## Abstract We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly (__ω__~1~ + 1)‐game‐closed forcings. PFA can be destroyed by a strongly (__ω__~1~ + 1)‐game‐closed forcing but not by an __ω__~2~‐closed. (© 2004 WILEY‐VCH Verlag GmbH & Co.