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Journal of Logic and Computation 2003 13(6):881-888; doi:10.1093/logcom/13.6.881
© 2003 by Oxford University Press
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Original Article

Comparing Constructive Arithmetical Theories Based on NP-PIND and coNP-PIND

Morteza Moniri

Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran; and Department of Mathematics, Shahid Beheshti University, Tehran, Iran. E-mail: ezmoniri{at}ipm.ir and ezmoniri{at}yahoo.com

In this note we show that the intuitionistic theory of polynomial induction on 1b+-formulas does not imply the intuitionistic theory I S21 of polynomial induction on {sum}1b+-formulas. We also show the converse assuming the Polynomial Hierarchy does not collapse. Similar results hold also for length induction in place of polynomial induction. We also investigate the relation between various other intuitionistic first-order theories of bounded arithmetic. Our method is mostly semantical, we use Kripke models of the theories.

Keywords: Intuitionistic bounded arithmetic, polynomial hierarchy, polynomial induction, length induction, NP-formulas, coNP-formulas, Kripke models

Received 9 December 2002.


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M. Moniri
On the Hierarchy of Intuitionistic Bounded Arithmetic
J Logic Computation, August 1, 2008; 18(4): 625 - 630.
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