  Computability theory is a discipline in the intersection of computer science
and mathematical logic where the fundamental question is:
  given two mathematical objects X and Y, does X compute Y in principle?
  In case X and Y are real numbers, Turing's famous 'machine' model provides
the standard interpretation of 'computation' for this question. To formalise
computation involving (total) abstract objects, Kleene introduced his S1-S9
computation schemes. In turn, Dag Normann and the author have introduced a
version of the lambda calculus involving fixed point operators that exactly
captures S1-S9 and accommodates partial objects. In this paper, we use this new
model to develop the computability theory of various well-known theorems due to
Baire and Volterra and related results; these theorems only require basic
mathematical notions like continuity, open sets, and density. We show that
these theorems due to Baire and Volterra are computationally equivalent from
the point of view of our new model, sometimes working in rather tame fragments
of Goedel's T.
