22 found
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  1.  73
    Model Theory of Modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
  2.  58
    Quasi Finitely Axiomatizable Totally Categorical Theories.Gisela Ahlbrandt & Martin Ziegler - 1986 - Annals of Pure and Applied Logic 30 (1):63-82.
  3. Stable Theories with a New Predicate.Enrique Casanovas & Martin Ziegler - 2001 - Journal of Symbolic Logic 66 (3):1127-1140.
  4.  29
    The 116 Reducts of (ℚ, <,A).Markus Junker & Martin Ziegler - 2008 - Journal of Symbolic Logic 73 (3):861-884.
    This article aims to classify those reducts of expansions of (Q, <) by unary predicates which eliminate quantifiers, and in particular to show that, up to interdefinability, there are only finitely many for a given language. Equivalently, we wish to classify the closed subgroups of Sym(Q) containing the group of all automorphisms of (Q, <) fixing setwise certain subsets. This goal is achieved for expansions by convex predicates, yielding expansions by constants as a special case, and for the expansion by (...)
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  5.  25
    Singular Coverings and Non‐Uniform Notions of Closed Set Computability.Stéphane Le Roux & Martin Ziegler - 2008 - Mathematical Logic Quarterly 54 (5):545-560.
    The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non-empty co-r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Lebesgue measure.This leads us to investigate for various classes of computable real subsets whether they always contain a computable point.
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  6.  9
    Stable Theories with a New Predicate.Enrique Casanovas & Martin Ziegler - 2001 - Journal of Symbolic Logic 66 (3):1127-1140.
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  7.  18
    An Exposition of Hrushovskiʼs New Strongly Minimal Set.Martin Ziegler - 2013 - Annals of Pure and Applied Logic 164 (12):1507-1519.
    We give an exposition of Hrushovskiʼs New Strongly Minimal Set : A strongly minimal theory which is not locally modular but does not interpret an infinite field. We give an exposition of his construction.
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  8.  35
    Separably Closed Fields with Hasse Derivations.Martin Ziegler - 2003 - Journal of Symbolic Logic 68 (1):311-318.
    In [6] Messmer and Wood proved quantifier elimination for separably closed fields of finite Ershov invariant e equipped with a (certain) Hasse derivation. We propose a variant of their theory, using a sequence of e commuting Hasse derivations. In contrast to [6] our Hasse derivations are iterative.
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  9.  31
    What's so Special About (Z/4Z)Ω?Gisela Ahlbrandt & Martin Ziegler - 1991 - Archive for Mathematical Logic 31 (2):115-132.
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  10.  21
    Fusion Over a Vector Space.Andreas Baudisch, Amador Martin-Pizarro & Martin Ziegler - 2006 - Journal of Mathematical Logic 6 (2):141-162.
    Let T1 and T2 be two countable strongly minimal theories with the DMP whose common theory is the theory of vector spaces over a fixed finite field. We show that T1 ∪ T2 has a strongly minimal completion.
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  11.  26
    Real Computation with Least Discrete Advice: A Complexity Theory of Nonuniform Computability with Applications to Effective Linear Algebra.Martin Ziegler - 2012 - Annals of Pure and Applied Logic 163 (8):1108-1139.
  12.  12
    Computable Operators on Regular Sets.Martin Ziegler - 2004 - Mathematical Logic Quarterly 50 (45):392-404.
    For regular sets in Euclidean space, previous work has identified twelve ‘basic’ computability notions to which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural operations on regular sets: union, intersection, complement, convex hull, image, and pre-image under suitable classes of functions. It turns out that only few of these notions are suitable in the sense of rendering all those operations uniformly computable.
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  13.  14
    Algebraically Closed Groups of Large Cardinality.Saharon Shelah & Martin Ziegler - 1979 - Journal of Symbolic Logic 44 (4):522-532.
  14.  8
    An Exposition of the Compactness Of.Enrique Casanovas & Martin Ziegler - 2020 - Bulletin of Symbolic Logic 26 (3-4):212-218.
    We give an exposition of the compactness of L(QcfC), for any set C of regular cardinals.
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  15.  29
    Pseudo-Finite Homogeneity and Saturation.Jörg Flum & Martin Ziegler - 1999 - Journal of Symbolic Logic 64 (4):1689-1699.
    When analyzing database query languages a roperty, of theories, the pseudo-finite homogeneity property, has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the finite cover property if and only if it has the pseudo-finite saturation property.
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  16.  6
    Equational Theories of Fields.Amador Martin-Pizarro & Martin Ziegler - 2020 - Journal of Symbolic Logic 85 (2):828-851.
    A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.
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  17.  23
    Computability on Regular Subsets of Euclidean Space.Martin Ziegler - 2002 - Mathematical Logic Quarterly 48 (S1):157-181.
    For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ‘weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide.
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  18.  20
    Pour Dire Un Mot, À la Fin, Pour Commencer.Werner Hamacher & Martin Ziegler - 2005 - Rue Descartes 48 (2):56.
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  19.  15
    On a Question of Herzog and Rothmaler.Anand Pillay & Martin Ziegler - 2004 - Journal of Symbolic Logic 69 (2):478-481.
  20.  10
    Barcelona, Catalonia, Spain July 11–16, 2011.Georges Gonthier, Martin Ziegler, Steve Awodey, George Barmpalias & Lev D. Beklemishev - 2012 - Bulletin of Symbolic Logic 18 (3).
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  21.  23
    Ein Rekursiv Aufzählbarer btt-Grad, der Nicht Zum Wortproblem Einer Gruppe Gehört.Martin Ziegler - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):165-168.
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  22.  12
    Ein Rekursiv Aufzählbarer btt‐Grad, der Nicht Zum Wortproblem Einer Gruppe Gehört.Martin Ziegler - 1976 - Mathematical Logic Quarterly 22 (1):165-168.
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