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math.LO2005
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…
math.LO2005
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…
math.LO2004
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…