A formal number-termed system based on recursion
Trevor J. McMinn · Rocky Mountain Journal of Mathematics · 1974
This is a formal number-termed axiomatization of number theory based on recursion without presupposing or developing general functional concepts or any part of set theory, together with an initial development to indicate its adequacy.The formal inferential system in which it is framed is that of A. P. Morse.The axioms, phrased in the primitive terms '0' and II xy u xy m n and the defined term 'scsr ri, are essentially (1) II xy u' xy m 0 = m, (2) II xy u'xy m scsr n = u'n II xy u'xy mn y (3) induction. Introduction.For full-blown (natural) number theory we require the capability of making recursive definitions.We need to define exponentiation and more generally arbitrary finite summation and multiplication, to introduce the Euler