Consider the following theorem of Koepke:
'A set x of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of the constructible universe L".
Taking the contrapositive of each implication in the above biconditional one has (this thanks to Andreas Blass):
'A set x of ordinals is not ordinal computable from a finite set of ordinal parameters if and only if it [i.e. x--my comment] is not constructible'.
A few questions spring to mind:
a) Can ordinal Turing machines only compute from a finite set of ordinal parmeters?
b) If not, can the ordinal computation (using ordinal Turing machines) of a set x of ordinals from an infinite set of ordinal parameters, if x can only be computed from an infinite set of ordinal parameters, imply that x is nonconstructible (from Prof. Blass' 'contrapositive' reformulation of Koepke's theorem, the answer would seem to be 'yes' since x is not computable from a finite set of ordinal parameters)?
c) What features would an ordinal Turing machine have to have in order to ordinal compute from an infinite set of ordinal parameters?
This is a reformulation of my earlier post on ordinal Turing machines which unfortunately was not well received. I hope this is a better formulation.