20 citations · 36 across the 10 of their papers we have counts for
24 papers
The modal logic of forcing
Joel David Hamkins, Benedikt Loewe
What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are natu…
The halting problem is decidable on a set of asymptotic probability one
Joel David Hamkins, Alexei Miasnikov
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptoti…
Diamond (on the regulars) can fail at any strongly unfoldable cardinal
Joel David Hamkins, Mirna Džamonja
If kappa is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which Diamond_kappa(REG) fails. This result continues the progression of the correspo…
The Necessary Maximality Principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
Joel David Hamkins, W. Hugh Woodin
The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain…
P is not equal to NP intersect coNP for Infinite Time Turing Machines
Vinay Deolalikar, Joel David Hamkins, Ralf-Dieter Schindler
Extending results of Schindler [math.LO/0106087] and Hamkins and Welch [math.LO/0212046], we establish in the context of infinite time Turing machines that P is properly contained…
Exactly controlling the non-supercompact strongly compact cardinals
Arthur W. Apter, Joel David Hamkins
We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many c…