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  • Joel David Hamkins
  • Mathematics, Computer Science
  • Minds and Machines
  • 21 August 1998
  • Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoreticalContinue Reading
  • Joel David Hamkins
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 28 September 2000
  • In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence phi holding in some forcing extension V^P andContinue Reading
  • Joel David Hamkins
  • Mathematics
  • 4 August 1998
  • In this paper, I generalize the landmark Lévy-Solovay Theorem [LévSol67], which limits the kind of large cardinal embeddings that can exist in a small forcing extension, to a broad new class ofContinue Reading
  • Joel David Hamkins
  • Mathematics, Computer Science
  • Ann. Pure Appl. Logic
  • 4 August 1998
  • Abstract The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or whatContinue Reading
  • Joel David Hamkins
  • Mathematics, Computer Science
  • Rev. Symb. Log.
  • 22 August 2011
  • The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe.Continue Reading