Ultrapowers without the axiom of choice

Journal of Symbolic Logic 53 (4):1208-1219 (1988)

Abstract
A new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice fails; this is arranged by means of an application of the omitting types theorem. The general theory of pseudo-ultrapowers is developed. Following that, we study supercompactness in the absence of choice, and we analyze pseudo-ultrapowers of models of the axiom of determinateness and various infinite exponent partition relations. Relationships between pseudo-ultrapowers and forcing are also discussed
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2274614
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 45,461
Through your library

References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
On the Determinacy of Games on Ordinals.L. A. Harrington - 1981 - Annals of Pure and Applied Logic 20 (2):109.
Magidor-Like and Radin-Like Forcing.J. M. Henle - 1983 - Annals of Pure and Applied Logic 25 (1):59-72.
Researches Into the World of "X" [Implies] "X".J. M. Henle - 1979 - Annals of Mathematical Logic 17 (1/2):151.
Model Theory for Infinitary Logic. Logic with Countable Conjunctions and Finite Quantifiers.[author unknown] - 1973 - Journal of Symbolic Logic 38 (3):522-523.

Add more references

Citations of this work BETA

Iterated Extended Ultrapowers and Supercompactness Without Choice.Mitchell Spector - 1991 - Annals of Pure and Applied Logic 54 (2):179-194.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
245 ( #28,015 of 2,280,310 )

Recent downloads (6 months)
2 ( #564,484 of 2,280,310 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature