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  1. ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
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  • On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
    We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal.
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  • Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
    We study the notion of dp-minimality, beginning by providing several essential facts about dp-minimality, establishing several equivalent definitions for dp-minimality, and comparing dp-minimality to other minimality notions. The majority of the rest of the paper is dedicated to examples. We establish via a simple proof that any weakly o-minimal theory is dp-minimal and then give an example of a weakly o-minimal group not obtained by adding traces of externally definable sets. Next we give an example of a divisible ordered Abelian (...)
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  • On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
    We study dp-minimal and strongly dependent theories and investigate connections between these notions and weight.
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  • 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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  • On uniform definability of types over finite sets.Vincent Guingona - 2012 - Journal of Symbolic Logic 77 (2):499-514.
    In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.
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  • Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory.Saharon Shelah - 1971 - Annals of Mathematical Logic 3 (3):271-362.
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  • Model theory of modules over a serial ring.Paul C. Eklof & Ivo Herzog - 1995 - Annals of Pure and Applied Logic 72 (2):145-176.
    We use the Drozd-Warfield structure theorem for finitely presented modules over a serial ring to investigate the model theory of modules over a serial ring, in particular, to give a simple description of pp-formulas and to classify the pure-injective indecomposable modules. We also study the question of whether every pure-injective indecomposable module over a valuation ring is the hull of a uniserial module.
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  • On Lascar rank and Morley rank of definable groups in differentially closed fields.Anand Pillay & Wai Yan Pong - 2002 - Journal of Symbolic Logic 67 (3):1189-1196.
    Morley rank and Lascar rank are equal on generic types of definable groups in differentially closed fields with finitely many commuting derivations.
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  • Categoricity and ranks.Jürgen Saffe - 1984 - Journal of Symbolic Logic 49 (4):1379-1392.
    In this paper we investigate the connections between categoricity and ranks. We use stability theory to prove some old and new results.
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  • Magidor-Malitz quantifiers in modules.Andreas Baudisch - 1984 - Journal of Symbolic Logic 49 (1):1-8.
    We prove the elimination of Magidor-Malitz quantifiers for R-modules relative to certain Q 2 α -core sentences and positive primitive formulas. For complete extensions of the elementary theory of R-modules it follows that all Ramsey quantifiers (ℵ 0 -interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no R-module having the finite cover property.
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  • On Decidable Extensions of Presburger Arithmetic: From A. Bertrand Numeration Systems to Pisot Numbers.Françoise Point - 2000 - Journal of Symbolic Logic 65 (3):1347-1374.
    We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.
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