6 papers · 1 filter
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…
Sufficient conditions for the forcing theorem, and turning proper classes into sets
Peter Holy, Regula Krapf, Philipp Schlicht
We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forci…
Characterizations of pretameness and the Ord-cc
Peter Holy, Regula Krapf, Philipp Schlicht
It is well known that pretameness implies the forcing theorem, and that pretameness is characterized by the preservation of the axioms of , that is wit…
Class forcing, the forcing theorem and Boolean completions
Peter Holy, Regula Krapf, Philipp Lücke +2
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is eve…
A hierarchy of Ramsey-like cardinals
Peter Holy, Philipp Schlicht
We introduce a hierarchy of large cardinals between weakly compact and measurable cardinals, that is closely related to the Ramsey-like cardinals introduced by Victoria Gitman, and…
Small Embedding Characterizations for Large Cardinals
Peter Holy, Philipp Lücke, Ana Njegomir
We show that many large cardinal notions can be characterized in terms of the existence of certain elementary embeddings between transitive set-sized structures, that map their cri…