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By Neil D. Jones

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Show that if a set is effectively enumerable, then it is effectively enumerable without repetitions. 3. Show that a set S φ 0 can be effectively enumerated in increasing order if and only if S is decidable. 4. Show that if S is the range of an effectively computable partial function, then S is effectively enumerable. 5. In what order does the algorithm of Proposition II. 6 enumerate the domain of a partial function gl 6. Show that if S and T are effectively enumerable (effectively decidable), then S u T and S n T are of the same type.

Xn) if it is scanning the leftmost symbol of x± * · · · * xn *, and is about to execute instruction il. This describes the standard input format for a Turing machine. We do not specify an output format rigidly but instead give a rule by which any configuration of Zmay be interpreted as containing an " o u t p u t " word from A*. Suppose the tape of Z is · · · * * αγα2 · · * am * * · · ·, where each at e A u {*}; suppose further that Z is currently scanning symbol ak. , am) are ignored for this purpose.

A) x is even, (b) x

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