Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/34577
Title: Parameter reduction in definition by multi-successor recursion.
Authors: Burville, J. C.
Award date: 1973
Presented at: University of Leicester
Abstract: It is well known that in primitive recursive arithmetic with a single successor the number of parameters in a definition by recursion may be successively reduced. In this thesis I examine the possibility of effecting a similar reduction in the number of parameters in a definition by recursion in a multi-successor arithmetic. The reduction process involves the discovery in multi-successor arithmetic of analogues of pairing functions and of functions which select the elements of an ordered pair. One of the difficulties in finding such functions is the construction within multi-successor arithmetic of suitable product and square foot functions and establishing the properties of these functions, and the pairing functions, within a formalisation of multi-successor arithmetic. The reduction process involves of course an examination of what functions, if any, need to be adjoined to the initial functions to secure the generality of the reduction.
Links: http://hdl.handle.net/2381/34577
Type: Thesis
Level: Doctoral
Qualification: Ph.D.
Rights: Copyright © the author. All rights reserved.
Appears in Collections:Theses, Dept. of Mathematics
Leicester Theses

Files in This Item:
File Description SizeFormat 
U391950.pdf3.98 MBAdobe PDFView/Open


Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.