Atomic models higher up

Annals of Pure and Applied Logic 155 (3):225-241 (2008)
  Copy   BIBTEX


There exists a countable structure of Scott rank where and where the -theory of is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its -theory. Most well-known models with unbounded atoms below also realize a non-principal -type; such a model that preserves the Σ1-admissibility of will have Scott rank . Makkai [M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 301–318. [4]] produces a hyperarithmetical model of Scott rank whose -theory is ω-categorical. A computable variant of Makkai’s example is produced in [W. Calvert, S.S. Goncharov, J.F. Knight, J. Millar, Categoricity of computable infinitary theories, Arch. Math. Logic . [1]; J. Knight, J. Millar, Computable structures of rank J. Math. Logic . [2]]



    Upload a copy of this work     Papers currently archived: 92,323

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Degree Spectra of Prime Models.Barbara F. Csima - 2004 - Journal of Symbolic Logic 69 (2):430 - 442.
On the existence of atomic models.M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1189-1194.
Generic Expansions of Countable Models.Silvia Barbina & Domenico Zambella - 2012 - Notre Dame Journal of Formal Logic 53 (4):511-523.
Atomic lexical entries.David Lightfoot - 1999 - Behavioral and Brain Sciences 22 (6):1029-1030.
The Financing Methods of Higher Education System.Birutė Pranevičienė & Aurelija Pūraitė - 2010 - Jurisprudencija: Mokslo darbu žurnalas 122 (4):335-356.
Atomic theory and the description of nature.Niels Bohr - 1934 - Woodbridge, Conn.: Ox Bow Press.
Evidence theory in multivalued models of modal logic.Elena Tsiporkova, Bernard De Baets & Veselka Boeva - 2000 - Journal of Applied Non-Classical Logics 10 (1):55-81.
Prime and atomic models.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (3):385-393.
The recently claimed observation of atomic orbitals and some related philosophical issues.Eric R. Scerri - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S76-.


Added to PP

8 (#1,323,642)

6 months
2 (#1,206,262)

Historical graph of downloads
How can I increase my downloads?

References found in this work

The α-finite injury method.G. E. Sacks & S. G. Simpson - 1972 - Annals of Mathematical Logic 4 (4):343-367.
Metarecursive sets.G. Kreisel & Gerald E. Sacks - 1965 - Journal of Symbolic Logic 30 (3):318-338.
An example concerning Scott heights.M. Makkai - 1981 - Journal of Symbolic Logic 46 (2):301-318.
Scott sentences and admissible sets.Mark Nadel - 1974 - Annals of Mathematical Logic 7 (2):267.

View all 7 references / Add more references