110 research outputs found
A partially non-proper ordinal beyond L(V \u3bb+1)
In his recent work, Woodin has defined new axioms stronger than I0 (the existence of an elementary embedding from to itself), that involve elementary embeddings between slightly larger models. There is a natural correspondence between I0 and Determinacy, but to extend this correspondence in the new framework we must insist that these elementary embeddings are proper. Previous results validated the definition, showing that there exist elementary embeddings that are not proper, but it was still open whether properness was determined by the structure of the underlying model or not. This paper proves that this is not the case, defining a model that generates both proper and non-proper elementary embeddings, and compare this new model to the older ones
LD-Algebras beyond i0
The algebra of embeddings at the I3 level has been deeply analyzed, but nothing is known algebra-wise for embeddings above I3. In this article, we introduce an operation for embeddings at the level of I0 and above, and prove that they generate an LD-algebra that can be quite different from the one implied by I3
Laver and set theory
In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip
I0 and rank-into-rank axioms
This is a survey about I0 and rank-into-rank axioms, with some previously unpublished proofs
The iterability hierarchy above I3
In this paper we introduce a new hierarchy of large cardinals between I3 and I2, the iterability hierarchy, and we prove that every step of it strongly implies the ones below
Generic I0 at \u2135\u3c9
In this paper we introduce a generic large cardinal akin to I0, together with the consequences of \u2135\u3c9being s uch ageneric large cardinal. In this case \u2135\u3c9is J\ub4onsson, and in a choiceless inner model many properties hold that arein contrast with pcf theory in ZFC
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