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
No citations found.
Similar books and articles
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.
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.
Vivian Charles Walsh (1967). On the Significance of Choice Sets with Incompatibilities. Philosophy of Science 34 (3):243-250.
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.
G. P. Monro (1983). On Generic Extensions Without the Axiom of Choice. Journal of Symbolic Logic 48 (1):39-52.
Mitchell Spector (1985). Model Theory Under the Axiom of Determinateness. Journal of Symbolic Logic 50 (3):773-780.
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 downloads8 ( #178,926 of 1,101,814 )
Recent downloads (6 months)2 ( #191,891 of 1,101,814 )
How can I increase my downloads?