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		5.21 Definition is called r.e. extendible just in case there is an r.e. index-able such that .

		5.22 Lemma TxtEx = [TxtEx]prudent if and only if every is r.e. extendible.

		5.23 Lemma is r.e. extendible.

		§5.3 Constraints on the Use of Information

		Each initial sequence T[n] of a text T provides partial information about the identity of content(T). The information embodied in T[n] may be factored into two components:

		(i) content(T[n]), that is, the subset of content(T) available to the scientist by the nth moment, and (ii) the order in which content(T[n]) occurs in T[n].

		Human learners operate under processing constraints that prevent them from fully exploiting either kind of information. The notion of memory limitation studied in Chapters 3 and 4 is an example of a strategy modeling the first kind of restriction. The next two strategies capture the second kind of limitation.

		§5.3.1 Set-driven Scientists

		A set-driven scientist is insensitive to the order in which data are presented.

		5.24 Definition (Wexler and Culicover [194])

		(a) M is set driven just in case for all  s , , if , then .

		(b) .

		Note that we consider only the global version of set-drivenness. It is easy to verify that , the collection of finite languages, is identified by a set-driven scientist.

		Identification of a language L requires identification of every text for L, and these texts constitute every possible ordering of L. This consideration encourages the belief that the internal order of a finite sequence plays little role in identifiability. However, the next proposition shows the belief to be unjustified.