- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Knight's model, its automorphism group, and characterizing the uncountable cardinals
Journal of Mathematical Logic 2 (01):113-144 (2002)
Abstract
We show that every ℵα can be characterized by the Scott sentence of some countable model; moreover there is a countable structure whose Scott sentence characterizes ℵ1 but whose automorphism group fails the topological Vaught conjecture on analytic sets. We obtain some partial information on Ulm type dichotomy theorems for the automorphism group of Knight's model.Other Versions
No versions found
Links
PhilArchive
External links
(no proxy)
Setup an account with your affiliations in order to access resources via your University's proxy server
Through your library
- Sign in / register and customize your OpenURL resolver
- Configure custom resolver
My notes
Similar books and articles
On automorphism groups of countable structures.Su Gao - 1998 - Journal of Symbolic Logic 63 (3):891-896.
A Galois correspondence for countable short recursively saturated models of PA.Erez Shochat - 2010 - Mathematical Logic Quarterly 56 (3):228-238.
Decoding in the automorphism group of a recursively saturated model of arithmetic.Ermek Nurkhaidarov - 2015 - Mathematical Logic Quarterly 61 (3):179-188.
Recovering ordered structures from quotients of their automorphism groups.M. Giraudet & J. K. Truss - 2003 - Journal of Symbolic Logic 68 (4):1189-1198.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.
Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence.Ioannis Souldatos - 2014 - Notre Dame Journal of Formal Logic 55 (4):533-551.
Automorphism Groups of Arithmetically Saturated Models.Ermek S. Nurkhaidarov - 2006 - Journal of Symbolic Logic 71 (1):203 - 216.
On interstices of countable arithmetically saturated models of Peano arithmetic.Nicholas Bamber & Henryk Kotlarski - 1997 - Mathematical Logic Quarterly 43 (4):525-540.
Reconstructing the Topology of the Elementary Self-embedding Monoids of Countable Saturated Structures.Christian Pech & Maja Pech - 2018 - Studia Logica 106 (3):595-613.
The automorphism group of a resplendent model.James H. Schmerl - 2012 - Archive for Mathematical Logic 51 (5-6):647-649.
Analytics
Added to PP
2012-09-02
Downloads
35 (#678,037)
6 months
6 (#572,300)
2012-09-02
Downloads
35 (#678,037)
6 months
6 (#572,300)
Historical graph of downloads
Citations of this work
Disjoint amalgamation in locally finite aec.John T. Baldwin, Martin Koerwien & Michael C. Laskowski - 2017 - Journal of Symbolic Logic 82 (1):98-119.
Complete Lω1,ω‐sentences with maximal models in multiple cardinalities.John Baldwin & Ioannis Souldatos - 2019 - Mathematical Logic Quarterly 65 (4):444-452.
Hanf numbers for extendibility and related phenomena.John T. Baldwin & Saharon Shelah - 2022 - Archive for Mathematical Logic 61 (3):437-464.
A Note on Counterexamples to the Vaught Conjecture.Greg Hjorth - 2007 - Notre Dame Journal of Formal Logic 48 (1):49-51.
References found in this work
Analytic equivalence relations and Ulm-type classifications.Greg Hjorth & Alexander S. Kechris - 1995 - Journal of Symbolic Logic 60 (4):1273-1300.
A complete L ω1ω-sentence characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
On automorphism groups of countable structures.Su Gao - 1998 - Journal of Symbolic Logic 63 (3):891-896.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-99fc7d78b-xhc6d uwo