By Larry M. Hyman

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**Example text**

I mention in particular [Spector 19621, [Kleene and Vesley 19651, [Howard and Kreisel 19661, [Kreisel 1968, 1968A1, [Myhill 19681, [Troelstra 1968, 19691, [Kreisel and Troelstra 19701. [Troelstra 19691 gives a survey of the subject with a good bibliography. 3. Finitary spreads O e f i n i t i o n . A spread M is finitary (is a f a n ) if the spreadlaw A M is such that only a finite number of one-member sequences are admissible and that for every admissible sequence al, . . , an there is only a finite number of values of k such that ul, .

I - 7 r). This solution is complete in the precise sense; that is, if ( p l , . . , p,,) is a vector such that for every vector (ql, . , 9,) contained in (3), pk # qk for at least one value of k , then Li(pl, . . , p,,) # b, for at least one value of i. , Th. 1. 3. Rank unknown If the equations (2) are homogeneous and of rank r , it follows that they have a (n-r)-parameter solution which is complete in the precise sense. However, if the rank is not known, it may occiir that we can find no solution apart from the null-solution, even if all n-rowed minors are 0.

The question how the components of the sequence are successively determined, whether by a law, by free choices, by throwing a die, or by some other means, is entirely irrelevant. Of course two questions arise here: Is the introduction of the concept of an ips lcgitiinate and is it expedient 1 The former question can be anuwered in the affirmative if the concept is sufficiently clear to be acceptable as n fundamental SPF’“ADS 33 notion in mathematics. NOW I presume that you have serious doubts about its clearness.