Switch to: Citations

References in:

Incompatible Ω-Complete Theories

Peter Koellner & W. Hugh Woodin

Journal of Symbolic Logic 74 (4):1155 - 1170 (2009)

Add references

You must login to add references.

On the question of absolute undecidability.Peter Koellner - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: essays for his centennial. Ithaca, NY: Association for Symbolic Logic. pp. 153-188.details The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH (...) Download Export citation Bookmark 39 citations
(1 other version)A Δ22 well-order of the reals and incompactness of L.Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.details A forcing poset of size 221 which adds no new reals is described and shown to provide a Δ22 definable well-order of the reals . The encoding of this well-order is obtained by playing with products of Aronszajn trees: some products are special while other are Suslin trees. The paper also deals with the Magidor–Malitz logic: it is consistent that this logic is highly noncompact. Download Export citation Bookmark 16 citations
Certain very large cardinals are not created in small forcing extensions.Richard Laver - 2007 - Annals of Pure and Applied Logic 149 (1-3):1-6.details The large cardinal axioms of the title assert, respectively, the existence of a nontrivial elementary embedding j:Vλ→Vλ, the existence of such a j which is moreover , and the existence of such a j which extends to an elementary j:Vλ+1→Vλ+1. It is known that these axioms are preserved in passing from a ground model to a small forcing extension. In this paper the reverse directions of these preservations are proved. Also the following is shown : if V is a model (...) Download Export citation Bookmark 27 citations
(1 other version)[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.details Download Export citation Bookmark 71 citations

1