Sh:100

• Shelah, S. (1980). Independence results. J. Symbolic Logic, 45(3), 563–573. DOI: 10.2307/2273423 MR: 583374
• Abstract:
  We introduce proper forcing and oracle cc. The specific independence problems addressed are: prove that the results of [Sh:c, Ch.VIII] are in a sense best poosible, that is the occurance of many cases is necessary because we cannot prove the natural results implying them all. In particular: (A): consistently , CH fail and for some complete f.o. $T \subseteq T_1$, Y$T$ is countable super-stable not ${\aleph_0}$-stable $T_1$ of cardinality ${\aleph_1}$ but the pseudo elementary class PC$(T,T_1)$ is categorical in ${\aleph_1}$

  (B) second a related result for $T$ the theory of dense linear order but the conclusion is only having a universal model in ${\aleph_1} < 2^ {\aleph_0}$

• published version (12p)

@article{Sh:100,
 author = {Shelah, Saharon},
 title = {{Independence results}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {45},
 number = {3},
 year = {1980},
 pages = {563--573},
 issn = {0022-4812},
 mrnumber = {583374},
 mrclass = {03E40 (03C45 03E35)},
 doi = {10.2307/2273423}
}