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		Because of memory limitation, it is easy to see that F converges on T and T' to the same F does index. Hence, since these two texts are for different members of , F not identify and hence does not identify .

		Proposition 3.34 shows that, compared to the original paradigm, the memory limited model of linguistic development makes a stronger claim about comparative grammar. This is because the latter model imposes a more stringent condition on the class of human languages: it must not only be identifiable, but identifiable by a memory-limited learner. Of course, this greater stringency represents progress only if children are in fact memory-limited in something like the fashion envisioned by Definition 3.32.

		§3.8.1 Fat Text

		It may be that in the long run every sentence of a given human language will be uttered indefinitely often. What effect would this have on learning?

		3.36 Definition (a) A text T is fat just in case for all , is infinite.

		(b) Let scientist F and be given. F identifies on fat text just in case for every fat text T for any , F identifies T. In this case, is identifiable on fat text.

		Thus, every number appearing in a fat text appears infinitely often. Since each fat text for a language L is also a text for L, it is obvious that every identifiable collection of languages is identifiable on fat text. The converse proposition is Exercise 3-15.

		Fat text is more interesting in the context of memory limitation. The next proposition shows that the former entirely compensates for the latter. We leave its proof as an advanced exercise.

		3.37 Proposition Suppose that is identifiable. Then some memory-limited scientist identifies on fat text.

		This concludes our discussion of language identification in the present chapter. Later paradigms bearing on will be variations of this first one, and the reader should interpret terminology and notation in the sense defined here unless there is indication to the contrary. The same may be said of our next paradigm, function identification, to which we now turn.