5 papers · 1 filter
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…