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		6-7 Motivated by the definition of Oex above, consider the following variation in the definition of scientists.

		6.32 Definition Suppose .

		(a) A scientist is a mapping from SEG to finite sets of programs.

		(b) A scientist M is said to FOexa-identify f (written: ) just in case there exists a nonempty finite set D such that the following hold:

		1. for some ,  j i=a f, and 2. for all but finitely many n, M(f[n]) = D.

		(c) .

		Show that Oexa = FOexa.

		6-8 Let and . Show that, for all n, . (This generalizes the Nonunion Theorem (Theorem 4.25.))

		6-9 Prove each of the following.

		(a) Let . If M TxtBca-identifies L, then there exists such that the following hold:

		1. ;

		2. WM( s ) =a L;

		3. .

		Such a  s  is called a TxtBca-locking sequence for M on L. (This is an analog of the locking sequence lemma (Theorem 3.22) for TxtBca-identification.)

		(b) For , .

		(c) .

		(d) .

		6-10 Consider the following variation on TxtBca-identification.