20 citations · 36 across the 10 of their papers we have counts for
6 papers · 2 filters
Post's problem for supertasks has both positive and negative solutions
Joel David Hamkins, Andrew Lewis
Recently we have introduced a new model of infinite computation by extending the operation of ordinary Turing machines into transfinite ordinal time. In this paper we will show tha…
How Tall is the Automorphism Tower of a Group?
Joel David Hamkins
The automorphism tower of a group is obtained by computing its automorphism group, the automorphism group of THAT group and so on, iterating transfinitely. Each group maps into the…
Infinite Time Turing Machines
Joel David Hamkins, Andy Lewis
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals.…
The Lottery Preparation
Joel David Hamkins
The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, o…
Universal Indestructibility
Arthur W. Apter, Joel David Hamkins
From a suitable large cardinal hypothesis, we provide a model with a supercompact cardinal in which universal indestructibility holds: every supercompact and partially supercompact…
Gap Forcing
Joel David Hamkins
Many of the most common reverse Easton iterations found in the large cardinal context, such as the Laver preparation, admit a gap at some small delta in the sense that they factor…