Notre Dame Journal of Formal Logic 39 (3):363-388 (1998)

Authors
Zlatan Damnjanovic
University of Southern California
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 over a fragment of intuitionistic arithmetic. The progressions are based on uniform reflection principles of bounded complexity iterated along initial segments of a primitive recursively formulated system of notations for constructive ordinals. A semiformal system closed under a primitive recursively restricted -rule is described and proved equivalent to the transfinite progressions with respect to the prenex sentences
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DOI 10.1305/ndjfl/1039182252
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References found in this work BETA

Transfinite Recursive Progressions of Axiomatic Theories.Solomon Feferman - 1962 - Journal of Symbolic Logic 27 (3):259-316.
Hilbert's Program and the Omega-Rule.Aleksandar Ignjatović - 1994 - Journal of Symbolic Logic 59 (1):322 - 343.
Iterated Reflection Principles and the Ω-Rule.Ulf R. Schmerl - 1982 - Journal of Symbolic Logic 47 (4):721-733.
Elementary Realizability.Zlatan Damnjanovic - 1997 - Journal of Philosophical Logic 26 (3):311-339.
Strictly Primitive Recursive Realizability, I.Zlatan Damnjanovic - 1994 - Journal of Symbolic Logic 59 (4):1210-1227.

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Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.

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