19 citations · 68 across the 29 of their papers we have counts for
41 papers
Failure of the -dichotomy for generalized Cantor spaces
Matteo Casarosa, Philipp Schlicht
Kechris, Solecki and Todorčević's -dichotomy characterizes Borel graphs that admit a Borel measurable coloring with countably many colors. We show that the analogue to the $G_…
Continuous images of closed sets in generalized Baire spaces
Philipp Lücke, Philipp Schlicht
Let be an uncountable cardinal with . Given a cardinal , we equip the set consisting of all functions from to with the topology whose basic open…
The open dihypergraph dichotomy for generalized Baire spaces and its applications
Philipp Schlicht, Dori Sziráki
The open graph dichotomy for a subset of the Baire space states that any open graph on either admits a coloring in countably many colors or contains a perfect compl…
Forcing over choiceless models and generic absoluteness
Daisuke Ikegami, Philipp Schlicht
We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove a…
Countable ranks at the first and second projective levels
Merlin Carl, Philipp Schlicht, Philip Welch
A rank is a notion in descriptive set theory that describes ranks such as the Cantor-Bendixson rank on the set of closed subsets of a Polish space, differentiability ranks on the s…
Asymmetric cut and choose games
Peter Holy, Philipp Schlicht, Christopher Turner +1
We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals…
Ideal Topologies in Higher Descriptive Set Theory
Peter Holy, Marlene Koelbing, Philipp Schlicht +1
We investigate generalizations of the topology of the higher Cantor space on , based on arbitrary ideals rather than the bounded ideal on . Our main focus is on the topolog…
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…
Uniformization and Internal Absoluteness
Sandra Müller, Philipp Schlicht
Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existenc…
Generalized Polish spaces at regular uncountable cardinals
Claudio Agostini, Luca Motto Ros, Philipp Schlicht
In the context of generalized descriptive set theory, we systematically compare and analyze various notions of Polish-like spaces and standard -Borel spaces for an uncountab…
Ordered Semiautomatic Rings with Applications to Geometry
Ziyuan Gao, Sanjay Jain, Ji Qi +3
The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geome…
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…
Decision times of infinite computations
Merlin Carl, Philipp Schlicht, Philip Welch
The decision time of an infinite time algorithm is the supremum of its halting times over all real inputs. The decision time of a set of reals is the least decision time of an algo…
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…
Coarse groups, and the isomorphism problem for oligomorphic groups
Andre Nies, Philipp Schlicht, Katrin Tent
Let denote the topological group of permutations of the natural numbers. We study the complexity of the isomorphism relation on classes of closed subgroups in…
Lebesgue's Density Theorem and definable selectors for ideals
Sandra Müller, Philipp Schlicht, David Schrittesser +1
We introduce a notion of density point and prove results analogous to Lebesgue's density theorem for various well-known ideals on Cantor space and Baire space. In fact, we isolate…
The isomorphism problem for tree-automatic ordinals with addition
Sanjay Jain, Bakhadyr Khoussainov, Philipp Schlicht +1
This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such…
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…
Reachability for infinite time Turing machines with long tapes
Merlin Carl, Benjamin Rin, Philipp Schlicht
Infinite time Turing machine models with tape length , denoted , strengthen the machines of Hamkins and Kidder [HL00] with tape length . A new phenomenon is that for som…
Canonical Truth
Merlin Carl, Philipp Schlicht
We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model of ZFC that is uniquely character…
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…
Characterizations of pretameness and the Ord-cc
Peter Holy, Regula Krapf, Philipp Schlicht
It is well known that pretameness implies the forcing theorem, and that pretameness is characterized by the preservation of the axioms of , that is wit…
Class forcing, the forcing theorem and Boolean completions
Peter Holy, Regula Krapf, Philipp Lücke +2
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is eve…