8 papers
-definability at higher cardinals: Thin sets, almost disjoint families and long well-orders
Philipp Lücke, Sandra Müller
Given an uncountable cardinal , we consider the question of whether subsets of the power set of that are usually constructed with the help of the Axiom of Choice are definab…
Strong unfoldability, shrewdness and combinatorial consequences
Philipp Lücke
We show that the notions of "strongly unfoldable cardinals", introduced by Villaveces in his model-theoretic studies of models of set theory, and "shrewd cardinals", introduced by…
Structural reflection, shrewd cardinals and the size of the continuum
Philipp Lücke
Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifi…
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…
Characterizing large cardinals through Neeman's pure side condition forcing
Peter Holy, Philipp Lücke, Ana Njegomir
We show that some of the most prominent large cardinal notions can be characterized through the validity of certain combinatorial principles at in forcing extensions by the p…
Partition properties for simply definable colourings
Philipp Lücke
We study partition properties for uncountable regular cardinals that arise by restricting partition properties defining large cardinal notions to classes of simply definable colour…
-definable subsets of
Philipp Lücke, Ralf Schindler, Philipp Schlicht
We study -definable sets (i.e. sets that are equal to the collection of all sets satisfying a certain -formula with parameter ) in the presence of large cardina…
Free groups and automorphism groups of infinite fields
Philipp Lücke, Saharon Shelah
Let λbe a cardinal with λ=λ^{\aleph_0} and p be either 0 or a prime number. We show that there are fields K_0 and K_1 of cardinality λand characteristic p such that the automorphis…