On the Complexity of Propositional Quantification in Intuitionistic Logic Author(s): Philip Kremer Source: The Journal of Symbolic Logic, Vol. 62, No. 2 (Jun., 1997), pp. 529-544 Published by: Association for Symbolic Logic Stable URL: http://www.jstor.org/stable/2275545 Accessed: 23/05/2009 19:10 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=asl. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact
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THE JOURNAL
OF SYMBOLIC
LoGic
Volume 62, Number 2, June 1997
ON THE COMPLEXITY OF PROPOSITIONAL QUANTIFICATION IN INTUITIONISTIC LOGIC
PHILIP
Abstract.
We define a propositionally
Kripke's semantics for propositional
KREMER
quantified
intuitionistic
intuitionistic
logic Her+ by a natural extension
of
logic. We then show that Har+ is recursively isomorphic
to full second order classical logic. Her+ is the intuitionistic
analogue of the modal systems S57r+, S47r+,
S4.27r+, K47r+, Tir+, K7r+ and Bir+, studied by Fine.
?1. Introduction. Kripke's [1963] semantics for propositional intuitionistic logic can be extended in a natural way to a language with propositional quantifiers. Kripke defines an intuitionistic model structure to be an ordered triple (g, K,
