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By R.B. Jensen, A. Prestel

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Additional info for Set Theory and Model Theory: Proceedings of an Informal Symposium Held at Bonn, June 1-3, 1979

Sample text

Each (countably T ~ is each treating rather T~ containing extensions some , produced with a branch T - v possibility . they x from b x on T T latter though b over T ~ which Zl-definitions is as associating branches. There branches. are (Hence, no checks some to 31 be made. Case As 3. 1 2 there T is succeeds ~ in three subcases. are initial in ~. 2 and T is be done. a limit point of S T Set TT = U{T~I~ 6 S N T}. The only non-trivial check to be made T concerns condition (ii).

A n c < and KM = L b e c a u s e be a-Erd~s indiscernibles a l s o be d o n e = C~I LB [ ~ ] for But ~ cannot the p a r t i t i o n in t e r m s Definition. ~B < is a - E r d ~ s set for < M is a g e n e - in K M. , (a)<~ c a n b e structures. We show now cardinals. Ol= , . 2: Let ~ ~ e be a limit model ~= type

1 2 there T is succeeds ~ in three subcases. are initial in ~. 2 and T is be done. a limit point of S T Set TT = U{T~I~ 6 S N T}. The only non-trivial check to be made T concerns condition (ii). 3 T = s(v). Then ~ = s(~), where This z- ([) is handled = v. There as are in section three 3. subcases to consider. 1 ~ is initial in S T Let T T = T -m. 2 Then ~ = s(~) There are q , y 6 T_, ~ ordinals has where checks to be made. 3 = n. For each pair x,y 6 T ~ such that T% and T - infinitely Case non-trivial ~ : s(q).

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