13 found
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  1. Quasi-o-Minimal Structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
    A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...)
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  2.  24
    Definable Homomorphisms of Abelian Groups in o-Minimal Structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.
    We investigate the group of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure . We prove the existence of a “large”, definable subgroup of . If contains an infinite definable set of homomorphisms then some definable subgroup of B admits a definable multiplication, making it into a field. As we show, all of this can be carried out not only in the underlying structure but also in any structure definable in.
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  3.  34
    A Structure Theorem for Semibounded Sets in the Reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.
  4.  22
    Returning to Semi-Bounded Sets.Ya'acov Peterzil - 2009 - Journal of Symbolic Logic 74 (2):597-617.
    An o-minimal expansion of an ordered group is called semi-bounded if there is no definable bijection between a bounded and an unbounded interval in it (equivalently, it is an expansion of the group by bounded predicates and group automorphisms). It is shown that every such structure has an elementary extension.
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  5.  18
    Additive Reducts of Real Closed Fields.David Marker, Ya'acov Peterzil & Anand Pillay - 1992 - Journal of Symbolic Logic 57 (1):109-117.
  6. Scope Dominance with Upward Monotone Quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.
    We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1 x Q2 y φ → Q2 y Q1 x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q1 is ∃ or Q2 is ∀ (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.
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  7.  22
    Interpretable Groups Are Definable.Pantelis E. Eleftheriou, Ya'acov Peterzil & Janak Ramakrishnan - 2014 - Journal of Mathematical Logic 14 (1):1450002.
    We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals. We discuss the general open question of elimination of imaginaries in an o-minimal structure.
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  8.  40
    Geometry, Calculus and Zil'ber's Conjecture.Ya'acov Peterzil & Sergei Starchenko - 1996 - Bulletin of Symbolic Logic 2 (1):72-83.
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  9.  18
    Expansions of Algebraically Closed Fields II: Functions of Several Variables.Ya'acov Peterzil & Sergei Starchenko - 2003 - Journal of Mathematical Logic 3 (01):1-35.
    Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is meromorphic (...)
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  10.  33
    A Question of Van Den Dries and a Theorem of Lipshitz and Robinson; Not Everything Is Standard.Ehud Hrushovski & Ya'acov Peterzil - 2007 - Journal of Symbolic Logic 72 (1):119 - 122.
    We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.
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  11.  10
    Euler Characteristic of Imaginaries in o-Minimal Structures.Sofya Kamenkovich & Ya'acov Peterzil - 2017 - Mathematical Logic Quarterly 63 (5):376-383.
    We define the notion of Euler characteristic for definable quotients in an arbitrary o-minimal structure and prove some fundamental properties.
    No categories
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  12.  9
    A Note on Stable Sets, Groups, and Theories with NIP.Alf Onshuus & Ya'acov Peterzil - 2007 - Mathematical Logic Quarterly 53 (3):295-300.
    Let M be an arbitrary structure. Then we say that an M -formula φ defines a stable set inM if every formula φ ∧ α is stable. We prove: If G is an M -definable group and every definable stable subset of G has U -rank at most n , then G has a maximal connected stable normal subgroup H such that G /H is purely unstable. The assumptions hold for example if M is interpretable in an o-minimal structure.More generally, (...)
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  13.  4
    Zilber's Conjecture for Some o-Minimal Structures Over the Reals.Ya'acov Peterzil - 1993 - Annals of Pure and Applied Logic 61 (3):223-239.
    We formulate an analogue of Zilber's conjecture for o-minimal structures in general, and then prove it for a class of o-minimal structures over the reals. We conclude in particular that if is an ordered reduct of ,<,+,·,ex whose theory T does not have the CF property then, given any model of T, a real closed field is definable on a subinterval of.
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