Characterizations of semicomputable sets of real numbers

We give some characterizations of semicomputability of sets of reals by programs in certain While programming languages over a topological partial algebra of reals. We show that such sets are semicomputable if and only if they are one of the following:(i)unions of effective sequences of disjoint algebraic open intervals;(ii)unions of effective sequences of rational open intervals;(iii)unions of effective sequences of algebraic open intervals. …