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**publisher and metadata sources**).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 theoretical… Continue Reading

The Levy-Solovay Theorem[8] 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 broad new class of forcing… Continue Reading

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 and… Continue Reading

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 of… Continue Reading

If an extension Vbar of V satisfies the delta approximation and cover properties for classes and V is a class in Vbar, then every suitably closed embedding j:Vbar to Nbar in Vbar with critical point… Continue Reading

A set theoretical assertion psi is forceable or possible, written lozenge psi, if psi holds in some forcing extension, and necessary, written square psi, if psi holds in all forcing extensions. In… Continue Reading

Abstract The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what… Continue Reading

15 September 2011

The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility… Continue Reading

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

24 July 2011

Abstract A ground of the universe V is a transitive proper class W ⊆ V , such that W ⊨ ZFC and V is obtained by set forcing over W, so that V = W [ G ] for some W-generic filter G ⊆ P ∈ W . The model… Continue Reading