Algebraically Generalized Recursive Function Theory
H. Raymond Strong · IBM Journal of Research and Development · 1968
The Uniformly Reflexive Structure (URS) introduced by E. G. Wagner is, for this paper, a nonassociative algebra consisting of a domain and a binary operation satisfying the following axioms: 0. (∃*)(∀a)[a·* = *·a = *]; 1. (∃ψ)(∀ a,b,c,d)[ψ ≠ * & ((a ≠ * & b ≠ * & c ≠ * & d ≠ *) →((a = d & (((ψ·a)·b)·c)·d = b) or (a ≠ d & (((ψ ·a)·b)·c)·d = c)))] ; and 2. (∃α)(∀b,c,d) [α ≠ ψ & ((b ≠ * & c ≠ * & d ≠ *) →((α·b)·c ≠ * & ((α·b)·c)· d = (b·d)·(c·d)))]. Wagner showed that these structures generalize much of Recursive Function Theory (RFT).