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Summer 1998 Strictly Primitive Recursive Realizability, II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$-Rule
Zlatan Damnjanovic
Notre Dame J. Formal Logic 39(3): 363-388 (Summer 1998). DOI: 10.1305/ndjfl/1039182252

Abstract

The notion of strictly primitive recursive realizability is further investigated, and the realizable prenex sentences, which coincide with primitive recursive truths of classical arithmetic, are characterized as precisely those provable in transfinite progressions $\{\mathrm{PRA}(b) \vert b \in \underline{\mathrm{O}}\}$ over a fragment $\mbox{PR-}(\Sigma^{0}_{1}\mbox{-IR})$ of intuitionistic arithmetic. The progressions are based on uniform reflection principles of bounded complexity iterated along initial segments of a primitive recursively formulated system $\mathrm{\underline{O}}$ of notations for constructive ordinals. A semiformal system closed under a primitive recursively restricted $\omega$-rule is described and proved equivalent to the transfinite progressions with respect to the prenex sentences.

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Zlatan Damnjanovic. "Strictly Primitive Recursive Realizability, II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$-Rule." Notre Dame J. Formal Logic 39 (3) 363 - 388, Summer 1998. https://doi.org/10.1305/ndjfl/1039182252

Information

Published: Summer 1998
First available in Project Euclid: 6 December 2002

zbMATH: 0971.03060
MathSciNet: MR1741544
Digital Object Identifier: 10.1305/ndjfl/1039182252

Subjects:
Primary: 03F30
Secondary: 03F55

Rights: Copyright © 1998 University of Notre Dame

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Vol.39 • No. 3 • Summer 1998
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