Ralf Schindler

collaborators

3 papers

math.LO2024

The transcendence degree of the reals over certain set-theoretical subfields

Azul Fatalini, Ralf Schindler

It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set $X$ of…

math.LO2024

Martin's Maximum $_{c}^{*, ++}$ in $P_{m a x}$ extensions of strong models of determinacy

Ralf Schindler, Taichi Yasuda

We study a strengthening of $MM^{++}$ which is called $MM^{*, ++}$ and which was introduced by Asperó and Schindler. We force its bounded version $\mathrm{MM}^…

math.LO2023

PFA and the definability of the nonstationary ideal

Stefan Hoffelner, Paul Larson, Ralf Schindler +1

We produce, relative to a $ZFC$ model with a supercompact cardinal, a $ZFC$ model of the Proper Forcing Axiom in which the nonstationary ideal on $ω_{1}$ is $Π_{1}$ -definab…

The transcendence degree of the reals over certain set-theoretical subfields

Martin's Maximumc∗,++​ in Pmax​ extensions of strong models of determinacy

PFA and the definability of the nonstationary ideal

Martin's Maximum $_{c}^{*, ++}$ in $P_{m a x}$ extensions of strong models of determinacy