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Primitive recursion, equality, and a universal set

Published online by Cambridge University Press:  04 March 2009

M. Pfender ,
M. Kröplin  and
D. Pape
M. Pfender
Affiliation:
Technische Universität Berlin, MA 7-3, Str. d. 17. Juni 136, D-10623 Berlin
M. Kröplin
Affiliation:
Technische Universität Berlin, MA 7-3, Str. d. 17. Juni 136, D-10623 Berlin
D. Pape
Affiliation:
Technische Universität Berlin, MA 7-3, Str. d. 17. Juni 136, D-10623 Berlin
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Abstract

Within a categorical framework for primitive recursion, equality between p.r. maps is shown to be definable by suitable p.r. equality predicates. Equivalence is shown between a direct categorical formalization of classical p.r. functions and p.r. maps in the sense of Lawvere and Freyd. An extension of the theory is shown to admit a ‘universal set’ containing all objects of the extended theory of subobjects.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 4 , Issue 3 , September 1994 , pp. 295 - 313
Copyright
Copyright © Cambridge University Press 1994

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