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  1. Pac Structures as Invariants of Finite Group Actions.Daniel Max Hoffmann & Piotr Kowalski - forthcoming - Journal of Symbolic Logic:1-36.
    We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property (...)
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  • The notion of independence in categories of algebraic structures, part I: Basic properties.Gabriel Srour - 1988 - Annals of Pure and Applied Logic 38 (2):185-213.
    We define a formula φ in a first-order language L , to be an equation in a category of L -structures K if for any H in K , and set p = {φ;i ϵI, a i ϵ H} there is a finite set I 0 ⊂ I such that for any f : H → F in K , ▪. We say that an elementary first-order theory T which has the amalgamation property over substructures is equational if every quantifier-free (...)
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  • The notion of independence in categories of algebraic structures, Part I: Basic properties.M. Srour - 1988 - Annals of Pure and Applied Logic 38 (2):185.
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  • Stable theories, pseudoplanes and the number of countable models.Anand Pillay - 1989 - Annals of Pure and Applied Logic 43 (2):147-160.
    We prove that if T is a stable theory with only a finite number of countable models, then T contains a type-definable pseudoplane. We also show that for any stable theory T either T contains a type-definable pseudoplane or T is weakly normal.
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  • The indiscernible topology: A mock zariski topology.Markus Junker & Daniel Lascar - 2001 - Journal of Mathematical Logic 1 (01):99-124.
    We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies. The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.
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  • A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
    We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.
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  • Semi-Equational Theories.Artem Chernikov & Alex Mennen - forthcoming - Journal of Symbolic Logic:1-32.
    We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.
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  • Comparing axiomatizations of free pseudospaces.Olaf Beyersdorff - 2009 - Archive for Mathematical Logic 48 (7):625-641.
    Independently and pursuing different aims, Hrushovski and Srour (On stable non-equational theories. Unpublished manuscript, 1989) and Baudisch and Pillay (J Symb Log 65(1):443–460, 2000) have introduced two free pseudospaces that generalize the well know concept of Lachlan’s free pseudoplane. In this paper we investigate the relationship between these free pseudospaces, proving in particular, that the pseudospace of Baudisch and Pillay is a reduct of the pseudospace of Hrushovski and Srour.
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