4 papers
Combinatorics in Higher Solovay Models
Alejandro Poveda, Sebastiano Thei
We construe the singular-cardinal analogue of the classical Solovay model. Starting with large cardinal assumptions in the realm of supercompactness, we show that the our inner mod…
The Baire and perfect set properties at singulars cardinals
Vincenzo Dimonte, Alejandro Poveda, Sebastiano Thei
We construct a model of ZFC with a singular cardinal such that every subset of in has both the -Perfect Set Property and the -Baire Prope…
Axiom and supercompactness
Alejandro Poveda
We produce a model where every supercompact cardinal is -supercompact with inaccessible targets. This is a significant improvement of the main identity-crises configuratio…
The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps
Mohammad Golshani, Alejandro Poveda
Assuming the existence of a strong cardinal , a weakly compact cardinal above it and we force a generic extension in which is a singular strong limit cardinal of…