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math.LO2021
-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…
math.LO2021
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…
math.LO2021
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…