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Journal of Logic and Computation Advance Access originally published online on September 27, 2006
Journal of Logic and Computation 2006 16(5):685-695; doi:10.1093/logcom/exl031
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

On Non-axiomatizability of Superintuitionistic Predicate Logics of Some Classes of Well-founded and Dually Well-founded Kripke Frames

Dmitrij Skvortsov

All-Russian Institute of Scientific and Technical Information, Molodogvardejskaja 22, korp. 3, kv. 29, Moscow 121351, Russia.

E-mail: skvortsovd{at}yandex.ru

The article presents general results on non-axiomatizability for superintuitionistic predicate logics. In particular, the logics of all well-ordered, all dually well-ordered, and all dually well-founded Kripke frames (in the semantics with nested and with constant domains) are Formula -hard, and the logic of all Kripke frames of finite height is not recursively axiomatizable (although it is known to be Formula -arithmetical). A result on Kripke-incompleteness is stated as well.

Keywords: Superintuitionistic predicate logics; recursive axiomatizability; {Pi}11 -hardness; Kripke semantics


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