on topological spaces via domain representations

The effective content of ordered fields is investigated using tools of computability theory and reverse mathematics. Computable ordered fields are constructed with various interesting computability theoretic properties. These include a computable ordered field for which the sums of squares are reducible to the halting problem, a computable ordered field with no computable set of multiplicatively archimedean class representatives, and a computable ordered field every transcendence basis of which is immune. The question of computable dimension for ordered fields is posed, and answered for archimedean fields, fields with finite transcendence basis, and some fields with infinite pure transcendence basis. Several results from the reverse mathematics of ordered rings and fields are extended. Computability Theory, Reverse Mathematics,