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A model and its subset

Ludomir Newelski

Journal of Symbolic Logic 57 (2):644-658 (1992)

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Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.details T is stable. We define the notion of meager regular type and prove that a meager regular type is locally modular. Assuming I < 2o and G is a definable abelian group with locally modular regular generics, we prove a counterpart of Saffe's conjecture. Using these results, for superstable T we prove the conjecture of vanishing multiplicities. Also, as a further application, in some additional cases we prove a conjecture regarding topological stability of pseudo-types over Q. Download Export citation Bookmark 12 citations
Relative Vaught's Conjecture for Some Meager Groups.Ludomir Newelski - 2007 - Notre Dame Journal of Formal Logic 48 (1):115-132.details Assume G is a superstable locally modular group. We describe for any countable model M of Th(G) the quotient group G(M) / Gm(M). Here Gm is the modular part of G. Also, under some additional assumptions we describe G(M) / Gm(M) relative to G⁻(M). We prove Vaught's Conjecture for Th(G) relative to Gm and a finite set provided that ℳ(G) = 1 and the ring of pseudoendomorphisms of G is finite. Download Export citation Bookmark
Non-isolated types in stable theories.Predrag Tanović - 2007 - Annals of Pure and Applied Logic 145 (1):1-15.details We introduce notions of strong and eventual strong non-isolation for types in countable, stable theories. For T superstable or small stable we prove a dichotomy theorem: a regular type over a finite domain is either eventually strongly non-isolated or is non-orthogonal to a NENI type . As an application we obtain the upper bound for Lascar’s rank of a superstable theory which is one-based or trivial, and has fewer than 20 non-isomorphic countable models. Download Export citation Bookmark 1 citation
A model and its subset: the uncountable case.Ludomir Newelski - 1995 - Annals of Pure and Applied Logic 71 (2):107-129.details Assume Q is a definable subset of a model of T. We define a notion of Q-isolated type, generalizing an earlier definition for countable Q. This notion is absolute. For superstable T, we give some sufficient conditions for the existence of Q-atomic models. We apply this to prove some results on weak categoricity over a predicate. Download Export citation Bookmark
1995 European Summer Meeting of the Association for Symbolic Logic.Johann A. Makowsky - 1997 - Bulletin of Symbolic Logic 3 (1):73-147.details Download Export citation Bookmark

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