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Journal of Logic and Computation Advance Access published online on September 11, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp046
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

A Remark on Superintuitionistic Predicate Logics of Kripke Frames with Constant and with Nested Domains

Dmitrij Skvortsov

All-Russian Institute of Scientific and Technical Information, Molodogvardejskaja 22, korp.3, kv.29, 121351, Moscow, Russia.
E-mail: skvortsovd{at}yandex.ru

Received 31 January 2009.


  Abstract

The superintuitionistic predicate logics (without or with equality) of all predicate Kripke frames with nested domains over a fixed poset W (a set of possible worlds) are embeddable in the logic (without equality) of all Kripke frames with constant domains over W. Therefore, Takano's result [13] on finite axiomatizability of the logic of Kripke frames with constant domains over the set of real numbers implies the recursive axiomatizability of the corresponding logics with nested domains. Other consequences are mentioned as well.

Keywords: Superintuitionistic predicate logics; Kripke semantics; recursive axiomatizability; embeddings


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