Notre Dame Journal of Formal Logic 35 (4):496-522 (1994)

Authors
Zlatan Damnjanovic
University of Southern California
Abstract
We study a hierarchy of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that -place functions in can be enumerated by a single function in , and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are predicates that are not in . Along the way the rudimentary predicates of Smullyan are classified as
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DOI 10.1305/ndjfl/1040408609
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References found in this work BETA

Concatenation as a Basis for Arithmetic.W. V. Quine - 1946 - Journal of Symbolic Logic 11 (4):105-114.
Elementary Realizability.Zlatan Damnjanovic - 1997 - Journal of Philosophical Logic 26 (3):311-339.
A Hierarchy of Primitive Recursive Functions.J. P. Cleave - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (22):331-346.
A Hierarchy of Primitive Recursive Functions.J. P. Cleave - 1963 - Mathematical Logic Quarterly 9 (22):331-346.
The Structure of Loop Programs and Subrecursive Hierarchies.Bernhard Goetze & Werner Nehrlich - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (14-18):255-278.

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Elementary Realizability.Zlatan Damnjanovic - 1997 - Journal of Philosophical Logic 26 (3):311-339.

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