David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 53 (4):1208-1219 (1988)
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Mitchell Spector (1991). Iterated Extended Ultrapowers and Supercompactness Without Choice. Annals of Pure and Applied Logic 54 (2):179-194.
Similar books and articles
Mitchell Spector (1985). Model Theory Under the Axiom of Determinateness. Journal of Symbolic Logic 50 (3):773-780.
G. P. Monro (1983). On Generic Extensions Without the Axiom of Choice. Journal of Symbolic Logic 48 (1):39-52.
Lorenz Halbeisen & Saharon Shelah (2001). Relations Between Some Cardinals in the Absence of the Axiom of Choice. Bulletin of Symbolic Logic 7 (2):237-261.
Vivian Charles Walsh (1967). On the Significance of Choice Sets with Incompatibilities. Philosophy of Science 34 (3):243-250.
Paul E. Howard, Arthur L. Rubin & Jean E. Rubin (1978). Independence Results for Class Forms of the Axiom of Choice. Journal of Symbolic Logic 43 (4):673-684.
Paul Howard & Jean E. Rubin (1995). The Axiom of Choice for Well-Ordered Families and for Families of Well- Orderable Sets. Journal of Symbolic Logic 60 (4):1115-1117.
Mitchell Spector (1991). Extended Ultrapowers and the Vopěnka-Hrbáček Theorem Without Choice. Journal of Symbolic Logic 56 (2):592-607.
Added to index2009-01-28
Total downloads70 ( #46,039 of 1,725,565 )
Recent downloads (6 months)61 ( #18,649 of 1,725,565 )
How can I increase my downloads?