Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/models-of-set-theory-with-definable-ordinals-T525QJlQSS
References (24)
-
K. McAloon (1971)
Consistency results about ordinal definabilityAnnals of Mathematical Logic, 2
-
R. Solovay (1970)
A model of set-theory in which every set of reals is Lebesgue measurable*Annals of Mathematics, 92
-
P. Cohen (1966)
Set Theory and the Continuum Hypothesis -
J. Barwise (1975)
Admissible sets and structures -
S. Simpson (1974)
Forcing and models of arithmetic, 43
-
(1970)
The prime ideal theorem does not imply the axiom of choice, Axiomatic Set Theory, Part I -
A. Miller (1984)
Review: Michael Morley, The Number of Countable ModelsJournal of Symbolic Logic, 49
-
(1973)
Minimal Models of ZF -
J. Mycielski (1995)
New set-theoretic axioms derived from a lean metamathematicsJournal of Symbolic Logic, 60
-
Urlich Felgner (1971)
Comparison of the axioms of local and universal choiceFundamenta Mathematicae, 71
-
H. Keisler (1971)
Model theory for infinitary logic -
M. Morley (1970)
The number of countable modelsJournal of Symbolic Logic, 35
-
G. Kreisel, Hao Wang (1955)
Some Applications of Formalized Consistency ProofsFundamenta Mathematicae, 42
-
H. Friedman (1975)
Large models of countable heightTransactions of the American Mathematical Society, 201
-
A. Enayat (1988)
UNDEFINABLE CLASSES AND DEFINABLE ELEMENTS IN MODELS OF SET THEORY AND ARITHMETIC, 103
-
S. Grigorieff (1975)
Intermediate Submodels and Generic Extensions in Set TheoryAnnals of Mathematics, 101
-
J. Mycielski (2003)
Axioms which imply GCHFundamenta Mathematicae, 176
-
A. Enayat (2004)
Leibnizian models of set theoryJournal of Symbolic Logic, 69
-
S. Shelah (1984)
Can you take Solovay’s inaccessible away?Israel Journal of Mathematics, 48
-
Chen Chang, H. Keisler (1966)
Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics -
J. Mycielski, S. Swierczkowski (1964)
On the Lebesgue measurability and the axiom of determinatenessFundamenta Mathematicae, 54
-
A. Enayat (2004)
On the Leibniz–Mycielski axiom in set theoryFundamenta Mathematicae, 181
-
A. Enayat (1984)
On certain elementary extensions of models of set theoryTransactions of the American Mathematical Society, 283
-
A. Enayat (2002)
Counting models of set theoryFundamenta Mathematicae, 174
- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-004-0256-9
- Publisher site
- See Article on Publisher Site
Abstract
A DO model (here also referred to a Paris model) is a model [InlineMediaObject not available: see fulltext.] of set theory all of whose ordinals are first order definable in [InlineMediaObject not available: see fulltext.]. Jeffrey Paris (1973) initiated the study of DO models and showed that (1) every consistent extension T of ZF has a DO model, and (2) for complete extensions T, T has a unique DO model up to isomorphism iff T proves V=OD. Here we provide a comprehensive treatment of Paris models. Our results include the following:
Journal
Archive for Mathematical Logic – Springer Journals
Published: Sep 1, 2004