Co-critical points of elementary embeddings

Journal of Symbolic Logic 50 (1):220-226 (1985)
  Copy   BIBTEX

Abstract

Probably the two most famous examples of elementary embeddings between inner models of set theory are the embeddings of the universe into an inner model given by a measurable cardinal and the embeddings of the constructible universeLinto itself given by 0#. In both of these examples, the “target model” is a subclass of the “ground model”. It is not hard to find examples of embeddings in which the target model is not a subclass of the ground model: ifis a generic ultrafilter arising from forcing with a precipitous ideal on a successor cardinalκ, then the ultraproduct of the ground model viacollapsesκ. Such considerations suggest a classification of how close the target model comes to “fitting inside” the ground model.Definition 1.1. LetMandNbe inner models of ZFC, and letj:M→Nbe an elementary embedding. Theco-critical pointofjis the least ordinalλ, if any exist, such that there isX⊆λ, X∈NbutX∉M. Such anXis called anew subsetofλ.It is easy to see that the co-critical point ofj:M→Nis a cardinal inN.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,140

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Elementary embeddings and infinitary combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
Standardization principle of nonstandard universes.Masahiko Murakami - 1999 - Journal of Symbolic Logic 64 (4):1645-1655.
On generic elementary embeddings.Moti Gitik - 1989 - Journal of Symbolic Logic 54 (3):700-707.
On elementary embeddings from an inner model to the universe.J. Vickers & P. D. Welch - 2001 - Journal of Symbolic Logic 66 (3):1090-1116.
Nonabsoluteness of elementary embeddings.Friedrich Wehrung - 1989 - Journal of Symbolic Logic 54 (3):774-778.
Indescribable cardinals and elementary embeddings.Kai Hauser - 1991 - Journal of Symbolic Logic 56 (2):439-457.
Skolem functions and elementary embeddings.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):94-98.

Analytics

Added to PP
2009-01-28

Downloads
23 (#501,534)

6 months
1 (#447,993)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.

Add more references