On many simple $T$'s for $SP^{(*)}$

by Shelah. [Sh:1065]

We return to the problem of classifying simple T 's by SP_T(lambda, mu) and SP^2_T(lambda, mu) (or with theta - not central here). Presently (2014.1.30) it seems that

we can prove: that at least consistently there are many classes of such (simple) T 's. See also [Sh:F1370]. (2015.5.03) We have

also tried in some instances to use freeness as in [KoSh:645],

but it seems now as in section 2 to just force for some T, starting with providing examples for some clear T 's and then iterating giving a ``solution'' for every ``problem'', i.e. {mathscr M},|M| = lambda for some other family of T 's. We may fix R but vary the S^N 's so the n_{bold p} 's.


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