10 papers · 1 filter
Forcing axioms via ground model interpretations
Philipp Schlicht, Christopher Turner
We study principles of the form: if a name is forced to have a certain property , then there is a ground model filter such that satisfies . We prove a general c…
Long Games and -Projective Sets
Juan P. Aguilera, Sandra Müller, Philipp Schlicht
We prove a number of results on the determinacy of -projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under compleme…
Descriptive properties of higher Kurepa trees
Philipp Lücke, Philipp Schlicht
We use generalizations of concepts from descriptive set theory to study combinatorial objects of uncountable regular cardinality, focussing on higher Kurepa trees and the represent…
How to have more things by forgetting how to count them
Asaf Karagila, Philipp Schlicht
Cohen's first model is a model of Zermelo--Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of C…
Preserving levels of projective determinacy by tree forcings
Fabiana Castiblanco, Philipp Schlicht
We prove that various classical tree forcings -- for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing -- preserve the statement that every…
Sufficient conditions for the forcing theorem, and turning proper classes into sets
Peter Holy, Regula Krapf, Philipp Schlicht
We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forci…