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  1. On linearly ordered structures of finite rank.Alf Onshuus & Charles Steinhorn - 2009 - Journal of Mathematical Logic 9 (2):201-239.
    O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all (...)
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  • Several perverse of positivity.Bruno Poizat - 2010 - Annals of Pure and Applied Logic 161 (6):812-816.
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  • Quelques effets pervers de la positivité.Bruno Poizat - 2010 - Annals of Pure and Applied Logic 161 (6):812-816.
    La Logique positive a été introduite au début de ce troisième millénaire par Itaï Ben Yaacov, qui y a été conduit par une nécessité interne à la Théorie des modèles. Dans ce contexte de validité du Théorème de compacité, l’absence de négation provoque des situations inhabituelles, comme celle des structures infinies qui ont une extension élémentaire maximale, que nous étudions ici.
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  • Supersimplicity and quadratic extensions.A. Martin-Pizarro & F. O. Wagner - 2009 - Archive for Mathematical Logic 48 (1):55-61.
    An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point.
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  • From stability to simplicity.Byunghan Kim & Anand Pillay - 1998 - Bulletin of Symbolic Logic 4 (1):17-36.
    §1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.The class of simple theories includes stable theories, but also many more, such as the theory of the random graph. Moreover, many of the theories of particular (...)
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  • On n-dependent groups and fields.Nadja Hempel - 2016 - Mathematical Logic Quarterly 62 (3):215-224.
    First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IPn property for all natural numbers n and certain properties of dependent valued fields extend to the n-dependent context.
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  • Definable valuations induced by multiplicative subgroups and NIP fields.Katharina Dupont, Assaf Hasson & Salma Kuhlmann - 2019 - Archive for Mathematical Logic 58 (7-8):819-839.
    We study the algebraic implications of the non-independence property and variants thereof on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” :1850007, 2018).
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  • Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
    We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. We also show that a bounded PAC field is simple. 1998 Published by Elsevier Science B.V. All rights reserved.
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  • Preface.Douglas Cenzer, Valentina Harizanov, David Marker & Carol Wood - 2009 - Archive for Mathematical Logic 48 (1):1-6.
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  • Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
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