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		opposing point of view, see Putnam [156] and Pullum [154]). In any case we shall later consider paradigms that incorporate rationality requirements in one or another sense (see Chapter 5).

		Definition 3.12 is slightly different from the criterion of successful performance that we introduced informally in Section 1.3. Our earlier criterion required the learner to produce a last, correct guess, and to cease guessing thereafter. It thus corresponds to the following version of identification, here labeled ''identification*."

		3.16 Definition Scientist F identifies* just in case for every text T for any , is finite and nonempty, and content(T) = WF(T[n) for the greatest . In this case is identifiable*.

		The reader can easily verify that the two criteria of success are equivalent in the sense of the next proposition.

		3.17 Proposition is identifiable if and only if is identifiable*.

		Identification* is one of many criteria that are transparently equivalent to identification; another is presented in Exercise 3-4. (Criteria that are not equivalent to identification arise in Chapter 6.)

		To close this section we record the identifiability of a collection of languages that. recalls the discussion of Section 1.3.

		3.18 Proposition Let . Then is identifiable.

		Proof: Given any , let x s  be the least such that . Let scientist F be defined by the condition that for all , F( s ) = the least index for N - { x s  }. It is clear that F identifies .

		§3.5 Identification as a Limiting Process

		Let scientist F identify text T, and let be given. We say that F "begins to identify T at moment n" just in case n is the least integer such that:

		(a)

		(b)