21 found
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  1.  92
    G-Compactness and Groups.Jakub Gismatullin & Ludomir Newelski - 2008 - Archive for Mathematical Logic 47 (5):479-501.
    Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an (...)
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  2.  30
    Topological Dynamics of Definable Group Actions.Ludomir Newelski - 2009 - Journal of Symbolic Logic 74 (1):50-72.
    We interpret the basic notions of topological dynamics in the model-theoretic setting, relating them to generic types of definable group actions and their generalizations.
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  3. A Model and its Subset.Ludomir Newelski - 1992 - Journal of Symbolic Logic 57 (2):644-658.
    We try to count the number of countable models M of T with a fixed set Q = φ (M) of realizations of a type φ. Also, for stable T, we define an ordinal rank M measuring multiplicity of types, with additivity properties similar to those of U-rank.
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  4. Small Profinite Groups.Ludomir Newelski - 2001 - Journal of Symbolic Logic 66 (2):859-872.
    We propose a model-theoretic framework for investigating profinite groups. Within this framework we define and investigate small profinite groups. We consider the question if any small profinite group has an open abelian subgroup.
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  5.  8
    Meager Forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
    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.
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  6.  10
    On Bounded Type-Definable Equivalence Relations.Ludomir Newelski & Krzysztof Krupi?Ski - 2002 - Notre Dame Journal of Formal Logic 43 (4):231-242.
    We investigate some topological properties of the spaces of classes of bounded type-definable equivalence relations.
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  7.  4
    Topological Dynamics of Stable Groups.Ludomir Newelski - 2014 - Journal of Symbolic Logic 79 (4):1199-1223.
    AssumeGis a group definable in a modelMof a stable theoryT. We prove that the semigroupSG of completeG-types overMis an inverse limit of some semigroups type-definable inMeq. We prove that the maximal subgroups ofSG are inverse limits of some definable quotients of subgroups ofG. We consider the powers of types in the semigroupSG and prove that in a way every type inSG is profinitely many steps away from a type in a subgroup ofSG.
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  8. Scott Analysis of Pseudotypes.Ludomir Newelski - 1993 - Journal of Symbolic Logic 58 (2):648-663.
    This is a continuation of [N2]. We find a Borel definition of Q-isolation. We pursue a topological and Scott analysis of pseudotypes on S(Q).
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  9.  13
    Boundedness and Absoluteness of Some Dynamical Invariants in Model Theory.Krzysztof Krupiński, Ludomir Newelski & Pierre Simon - 2019 - Journal of Mathematical Logic 19 (2):1950012.
    Let [Formula: see text] be a monster model of an arbitrary theory [Formula: see text], let [Formula: see text] be any tuple of bounded length of elements of [Formula: see text], and let [Formula: see text] be an enumeration of all elements of [Formula: see text]. By [Formula: see text] we denote the compact space of all complete types over [Formula: see text] extending [Formula: see text], and [Formula: see text] is defined analogously. Then [Formula: see text] and [Formula: see (...)
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  10.  32
    Omitting Types and the Real Line.Ludomir Newelski - 1987 - Journal of Symbolic Logic 52 (4):1020-1026.
    We investigate some relations between omitting types of a countable theory and some notions defined in terms of the real line, such as for example the ideal of meager subsets ofR. We also try to express connections between the logical structure of a theory and the existence of its countable models omitting certain families of types.It is well known that assuming MA we can omit (...))
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  11.  14
    Weakly Minimal Formulas: A Global Approach.Ludomir Newelski - 1990 - Annals of Pure and Applied Logic 46 (1):65-94.
  12.  13
    Very Simple Theories Without Forking.Ludomir Newelski - 2003 - Archive for Mathematical Logic 42 (6):601-616.
    We prove Vaught's conjecture for minimal trivial simple theories satisfying the generalized independence theorem.
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  13.  25
    Definable Sets in Boolean-Ordered o-Minimal Structures. I.Ludomir Newelski & Roman Wencel - 2001 - Journal of Symbolic Logic 66 (4):1821-1836.
    We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.
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  14.  27
    On Atomic or Saturated Sets.Ludomir Newelski - 1996 - Journal of Symbolic Logic 61 (1):318-333.
    Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable and (bounded, 1-based or of (...)
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  15.  18
    Flat Morley Sequences.Ludomir Newelski - 1999 - Journal of Symbolic Logic 64 (3):1261-1279.
    Assume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within (...)
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  16.  19
    Omitting Types for Stable CCC Theories.Ludomir Newelski - 1990 - Journal of Symbolic Logic 55 (3):1037-1047.
  17.  30
    Geometry of *-Finite Types.Ludomir Newelski - 1999 - Journal of Symbolic Logic 64 (4):1375-1395.
    Assume T is a superstable theory with $ countable models. We prove that any *-algebraic type of M-rank > 0 is m-nonorthogonal to a *-algebraic type of M-rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of M-rank 1. We prove that after some localization this geometry becomes projective over a division ring F. Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that F (...)
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  18.  17
    A Model and its Subset: The Uncountable Case.Ludomir Newelski - 1995 - Annals of Pure and Applied Logic 71 (2):107-129.
    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.
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  19.  15
    On Partitions of the Real Line Into Compact Sets.Ludomir Newelski - 1987 - Journal of Symbolic Logic 52 (2):353-359.
  20.  11
    Relative Vaught's Conjecture for Some Meager Groups.Ludomir Newelski - 2007 - Notre Dame Journal of Formal Logic 48 (1):115-132.
    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.
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  21.  7
    Modular Types in Some Supersimple Theories.Ludomir Newelski - 2002 - Journal of Symbolic Logic 67 (4):1601-1615.