We describe a programming language IND that generalizes alternating Turing machines to
arbitrary first-order structures. We show that IND programs (resp. everywhere-halting IND
programs, loop-free IND programs) accept precisely the inductively definable (resp.
hyperelementary, elementary) relations. We give several examples showing how the
language provides a robust and computational approach to the theory of first-order inductive
definability. We then show:(1) on all acceptable structures (in the sense of Moschovakis …

We introduce a programming language IND that generalizes alternating Turing machines to
arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting
IND programs, loop-free IND programs) accept precisely the inductively definable
(respectively, hyperelementary, elementary) relations. We give several examples showing
how the language provides a robust and computational approach to the theory of first-order
inductive definability. We then show:(1) on all acceptable structures (in the sense of …