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Independent Sets of Axioms In Lκα

Published online by Cambridge University Press:  20 November 2018

Xavier Caicedo
Xavier Caicedo*
Affiliation:
Departamento de Mateméticas, Universidad de Los Andes Apartado Aéreo4976 Bogota D. E., Colombia
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A set of sentences T is called independent if for every . It is countably independent if every countable subset is independent. In flnitary first order logic, Lωω, the two notions coincide because of compactness. This is not the case for infinitary logic.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 219 - 223
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Barwise, K. J., Axioms for abstract Model Theory, Annals of Math. Logic, 7, 221. 265 (1974).Google Scholar
2. López-Escobar, E. G. K., An interpolation theorem for denumerably long formulas, Fundamenta Mathematicae, LVII, 253. 272 (1965).Google Scholar
3. Reznikoff, M. I., Tout ensemble de formules de la logique classique est equivalent á un ensemble independant, C.R. Acad. Se. Paris, 260, 2385. 2388 (1965).Google Scholar
4. Rubin, J. E., Set theory for the Mathematician, (1967).Google Scholar
(5) Tarski, A., Note in C. R. Soc. Se. Letters Varsovie III, 23 (1923).Google Scholar