12 papers
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…
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…
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…
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…