arXiv subjects
Publications and source records attributed to Salvatore Caporaso.
The recursion theorem in the weak form {e}(z)=x(e,z) (universal function not needed) and in Rogers form {n}(z)={{x}(n)}(z) and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.
A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n^c) and TIMEF(n_c); the finite Grzegorczyk classes at and above the elementary level, and the Σ_k-IND fragments of PA. Limited operators, diagonalization, and majorization functions are not used.