20 citations · 36 across the 10 of their papers we have counts for
5 papers · 2 filters
Unfoldable cardinals and the GCH
Joel David Hamkins
Introducing unfoldable cardinals last year, Andres Villaveces ingeniously extended the notion of weak compactness to a larger context, thereby producing a large cardinal notion, un…
Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
Arthur W. Apter, Joel David Hamkins
We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling th…
Infinite time Turing machines with only one tape
Joel David Hamkins, Daniel Evan Seabold
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same…
The Wholeness Axioms and V=HOD
Joel David Hamkins
The Wholeness Axioms, proposed by Paul Corazza, axiomatize the existence of an elementary embedding j:V-->V. Formalized by augmenting the usual language of set theory with an addit…
Gap forcing: generalizing the Levy-Solovay theorem
Joel David Hamkins
The landmark Levy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a br…