It is well known that complete number theory, i.e. the theory of the structure (FU, =, +, x ), is undecidable. When we drop one of the operations + or x , the theories Th(N, =, +) and Th(N, =, x) we obtain are decidable [19,16, 251. The computational complexity of these theories has been studied [3,4,8-l 1, 17, 18,20,21], eventually showing that Th( N, =, + ) is complete for uC,0 ATIME-ALT(2”“, n), and Th( N, =, x ) is complete for UC,0 ATIME-ALT(222’M, n) [S]. Many relations and functions can… CONTINUE READING