Hostname: page-component-6bf8c574d5-685pp Total loading time: 0 Render date: 2025-03-07T02:41:08.915Z Has data issue: false hasContentIssue false
  • English
  • Français

Dimension and finite closure

Published online by Cambridge University Press:  09 April 2009

W. F. Gross
W. F. Gross
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If is a model with dimension and finite closure, then T() is No-categorical. If is atomic, has dimension and finitely many algebraic elements, then has finite closure or a finite basis. If has finite closure, satisfies the Exchange Lemma, and one-one maps between independent subsets are elementary, then has dimension.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 421 - 430
Copyright
Copyright © Australian Mathematical Society 1977

References

Crossley, J. N. and Nerode, Anil (1974), Combinatorial Functors (Springer-Verlag, 1974).CrossRefGoogle Scholar
Ryll-Nardzewski, C. (1959), ‘On theories categorical in power No’, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 7, 545–548.Google Scholar