10 citations · 21 across the 16 of their papers we have counts for
18 papers
The effects of forcing on exacting and ultraexacting cardinals
Philipp Lücke, Alejandro Poveda
Motivated by recent work of Aguilera--Bagaria--Lücke and Aguilera--Bagaria--Goldberg--Lücke (ABGL), we analyze various effects of set-theoretic forcing upon the classes of exacting…
Large cardinals beyond HOD
Juan Pablo Aguilera, Joan Bagaria, Gabriel Goldberg +1
Exacting and ultraexacting cardinals are large cardinal numbers compatible with the Zermelo-Fraenkel axioms of set theory, including the Axiom of Choice. In contrast with standard…
Large cardinals, structural reflection, and the HOD Conjecture
Juan P. Aguilera, Joan Bagaria, Philipp Lücke
We introduce exacting cardinals and a strengthening of these, ultraexacting cardinals. These are natural large cardinals defined equivalently as weak forms of rank-Berkeley cardina…
The complexity of non-stationary ideals
Philipp Lücke
We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal can be defined by a -formula using parameters of h…
Outward compactness
Peter Holy, Philipp Lücke, Sandra Müller
We introduce and study a new type of compactness principle for strong logics that, roughly speaking, infers the consistency of a theory from the consistency of its small fragments…
Descriptive properties of I2-embeddings
Vincenzo Dimonte, Martina Iannella, Philipp Lücke
We contribute to the study of generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set of a singul…
On -Definable Closed Unbounded Sets
Omer Ben-Neria, Philipp Lücke
Definable stationary sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily…
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…
Patterns of Structural Reflection in the large-cardinal hierarchy
Joan Bagaria, Philipp Lücke
We unveil new patterns of Structural Reflection in the large-cardinal hierarchy below the first measurable cardinal. Namely, we give two different characterizations of strongly unf…
Non-absoluteness of Hjorth's Cardinal Characterization
Philipp Lücke, Ioannis Souldatos
In [5], Hjorth proved that for every countable ordinal , there exists a complete -sentence that has models of all cardinalities less than or equal to…
Huge Reflection
Joan Bagaria, Philipp Lücke
We study Structural Reflection beyond Vopěnka's Principle, at the level of almost-huge cardinals and higher, up to rank-into-rank embeddings. We identify and classify new large car…
Forcing axioms and the complexity of non-stationary ideals
Sean Cox, Philipp Lücke
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on and its restrictions to certain cofinalities. Our main result shows that the…
Closure properties of measurable ultrapowers
Philipp Lücke, Sandra Müller
We study closure properties of measurable ultrapowers with respect to Hamkin's notion of "freshness" and show that the extent of these properties highly depends on the combinatoria…
Small models, large cardinals, and induced ideals
Peter Holy, Philipp Lücke
We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will…
Squares, ascent paths, and chain conditions
Chris Lambie-Hanson, Philipp Lücke
With the help of various square principles, we obtain results concerning the consistency strength of several statements about trees containing ascent paths, special trees, and stro…
Measurable cardinals and good -wellorderings
Philipp Lücke, Philipp Schlicht
We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals with the property that the collection of all in…
Characterizing large cardinals in terms of layered posets
Sean Cox, Philipp Lücke
Given an uncountable regular cardinal , a partial order is -stationarily layered if the collection of regular suborders of of cardinality less than is statio…
The Hurewicz dichotomy for generalized Baire spaces
Philipp Luecke, Luca Motto Ros, Philipp Schlicht
By classical results of Hurewicz, Kechris and Saint-Raymond, an analytic subset of a Polish space is covered by a subset of if and only if it does not contain a close…