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  1.  39
    Definability in low simple theories.Ziv Shami - 2000 - Journal of Symbolic Logic 65 (4):1481-1490.
  2.  9
    On the forking topology of a reduct of a simple theory.Ziv Shami - 2020 - Archive for Mathematical Logic 59 (3-4):313-324.
    Let T be a simple L-theory and let \ be a reduct of T to a sublanguage \ of L. For variables x, we call an \-invariant set \\) in \ a universal transducer if for every formula \\in L^-\) and every a, $$\begin{aligned} \phi ^-\ L^-\text{-forks } \text{ over }\ \emptyset \ \text{ iff } \Gamma \wedge \phi ^-\ L\text{-forks } \text{ over }\ \emptyset. \end{aligned}$$We show that there is a greatest universal transducer \ and it is type-definable. In (...)
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  3.  14
    On analyzability in the forking topology for simple theories.Ziv Shami - 2006 - Annals of Pure and Applied Logic 142 (1):115-124.
    We show that in a simple theory T in which the τf-topologies are closed under projections every type analyzable in a supersimple τf-open set has ordinal SU-rank. In particular, if in addition T is unidimensional, the existence of a supersimple unbounded τf-open set implies T is supersimple. We also introduce the notion of a standard τ-metric and show that for simple theories its completeness is equivalent to the compactness of the τ-topology.
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  4.  23
    Internality and interpretable automorphism groups in simple theories.Ziv Shami - 2004 - Annals of Pure and Applied Logic 129 (1-3):149-162.
    The binding group theorem for stable theories is partially extended to the simple context. Some results concerning internality are proved. We also introduce a ‘small’ normal subgroup G0+ of the automorphism group and show that if p is Q-internal then it has a finite exponent and G/G0+ is interpretable.
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  5.  17
    Coordinatisation by Binding Groups and Unidimensionality in Simple Theories.Ziv Shami - 2004 - Journal of Symbolic Logic 69 (4):1221 - 1242.
    In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence ( $a_{i}|i \leq n^{*}$ ) $\subseteq dcl^{eq}$ (a) with $a_{n}*$ = a such that for every $i \leq n*$ , if $p_{i} = tp(a_{i}/{a_{i}|j < i}$ ) then $Aut(p_{i}/Q)$ is type-definable with its action on $p_{i}^{c}$ . A unidimensional simple theory eliminates the quantifier $\exists^{\infty}$ and either interprets (in $C^{eq}$ ) an infinite type-definable group (...)
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  6.  21
    On Kueker Simple Theories.Ziv Shami - 2005 - Journal of Symbolic Logic 70 (1):216 - 222.
    We show that a Kueker simple theory eliminates Ǝ∞ and densely interprets weakly minimal formulas. As part of the proof we generalize Hrushovski's dichotomy for almost complete formulas to simple theories. We conclude that in a unidimensional simple theory an almost-complete formula is either weakly minimal or trivially-almost-complete. We also observe that a small unidimensional simple theory is supersimple of finite SU-rank.
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  7.  24
    On uncountable hypersimple unidimensional theories.Ziv Shami - 2014 - Archive for Mathematical Logic 53 (1-2):203-210.
    We extend the dichotomy between 1-basedness and supersimplicity proved in Shami :309–332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami :309–332, 2011)]. We conclude that every hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the (...)
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  8.  18
    Invariant Version of Cardinality Quantifiers in Superstable Theories.Alexander Berenstein & Ziv Shami - 2006 - Notre Dame Journal of Formal Logic 47 (3):343-351.
    We generalize Shelah's analysis of cardinality quantifiers for a superstable theory from Chapter V of Classification Theory and the Number of Nonisomorphic Models. We start with a set of bounds for the cardinality of each formula in some general invariant family of formulas in a superstable theory (in Classification Theory, a uniform family of formulas is considered) and find a set of derived bounds for all formulas. The set of derived bounds is sharp: up to a technical restriction, every model (...)
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  9.  71
    On the Type-Definability of the Binding Group in Simple Theories.Bradd Hart & Ziv Shami - 2005 - Journal of Symbolic Logic 70 (2):379 - 388.
    Let T be simple, work in Ceq over a boundedly closed set. Let p ∈ S(θ) be internal in a quasi-stably-embedded type-definable set Q (e.g., Q is definable or stably-embedded) and suppose (p, Q) is ACL-embedded in Q (see definitions below). Then Aut(p/Q) with its action on pC is type-definable in Ceq over θ. In particular, if p ∈ S(θ) is internal in a stably-embedded type-definable set Q, and pC υ Q is stably-embedded, then Aut(p/Q) is type-definable with its action (...)
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  10.  7
    A note on edge colorings and trees.Adi Jarden & Ziv Shami - 2022 - Mathematical Logic Quarterly 68 (4):447-457.
    We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies. Another result is that an uncountable cardinal κ is weakly compact if and only if κ is regular, has the tree property, and for each (...)
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  11.  11
    A note on the non‐forking‐instances topology.Ziv Shami - 2020 - Mathematical Logic Quarterly 66 (3):336-340.
    The non‐forking‐instances topology (NFI topology) is a topology on the Stone space of a theory T that depends on a reduct of T. This topology has been used in [6] to describe the set of universal transducers for (invariants sets that translate forking‐open sets in to forking‐open sets in T). In this paper we show that in contrast to the stable case, the NFI topology need not be invariant over parameters in but a weak version of this holds for any (...)
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  12.  29
    On the binding group in simple theories.Ziv Shami & Frank O. Wagner - 2002 - Journal of Symbolic Logic 67 (3):1016-1024.
    We show that if p is a real type which is almost internal in a formula φ in a simple theory, then there is a type p' interalgebraic with a finite tuple of realizations of p, which is generated over φ. Moreover, the group of elementary permutations of p' over all realizations of φ is type-definable.
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