## Journal of Symbolic Logic

### Semiproper Forcing Axiom Implies Martin Maximum but Not $|mathrm{PFA}^+$

Saharon Shelah

#### Abstract

We prove that MM (Martin maximum) is equivalent (in ZFC) to the older axiom SPFA (semiproper forcing axiom). We also prove that SPFA does not imply $SPFA^+$ or even $PFA^+$ (using the consistency of a large cardinal).

#### Article information

Source
J. Symbolic Logic, Volume 52, Issue 2 (1987), 360-367.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742365

Mathematical Reviews number (MathSciNet)
MR890443

Zentralblatt MATH identifier
0625.03035

JSTOR
Shelah, Saharon. Semiproper Forcing Axiom Implies Martin Maximum but Not $|mathrm{PFA}^+$. J. Symbolic Logic 52 (1987), no. 2, 360--367. https://projecteuclid.org/euclid.jsl/1183742365