Elementary Functions and LOOP Programs

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