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Independence results

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Hebrew University, Jerusalem, Israel University of Wisconsin, Madison, Wisconsin 53706 University of California, Berkeley, California 94720


We prove independence results concerning the number of nonisomorphic models (using the S-chain condition and S-properness) and the consistency of “ there is a universal linear order of power ℵ1”. Most of these results were announced in [Sh 4], [Sh 5].

In subsequent papers we shall prove an analog f MA for forcing which does not destroy stationary subsets of ω1 investigate -properness for various filters and prove the consistency with G.C.H. of an axiom implying SH (for ℵ1), and connected results.

Research Article
Copyright © Association for Symbolic Logic 1980

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[B]Baumgartner, J., All ℵ1-dense sets of reals can be isomorphic, Fundamenta mathematicae, vol. 79 (1973), pp. 101106.CrossRefGoogle Scholar
[Sh 1]Shelah, S., Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978.Google Scholar
[Sh 2]Shelah, S., Models with second-order properties. III, Omitting types in λ+ for L(Q), Proceedings of the Berlin Workshop, July 1977, Archiv für Mathematische Logik (to appear).Google Scholar
[Sh 3]Shelah, S., It is consistent that /finite has no non-trivial automorphisms (preprint).Google Scholar
[Sh 4]Shelah, S., Whitehead problem, independence of categoricity simple theories and Boolean algebras, Notices of the American Mathematical Society, vol. 25 (1978), A441.Google Scholar
[Sh 5]Shelah, S., Iterated forcing and independence results, Notices of the American Mathematical Society, vol. 25 (1978), A497.Google Scholar
[ST]Solovay, R.M. and Tenenbaum, S., Iterated Cohen extensions and Souslin's problem, Annals of Mathematics, vol. 94 (1971), pp. 201245.CrossRefGoogle Scholar
[W]Wimmers, E., The Shelah P-point independence theorem, Israel Journal of Mathematics (to appear).Google Scholar