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All intermediate logics with extra axioms in one variable, except eight, are not strongly ω-complete

Published online by Cambridge University Press:  12 March 2014

Camillo Fiorentini
Camillo Fiorentini*
Affiliation:
Dipartimento di Scienze dell'Informazione, Università Degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy, E-mail:fiorenti@dsi.unimi.it
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Abstract

In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.

Keywords

ω-canonicityextensive ω-canonicitystrong ω-completeness
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1576 - 1604
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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