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Mike Prest [16]M. Prest [4]
  1.  26
    Imaginary modules.T. G. Kucera & M. Prest - 1992 - Journal of Symbolic Logic 57 (2):698-723.
  2.  14
    Remarks on elementary duality.Mike Prest - 1993 - Annals of Pure and Applied Logic 62 (2):183-205.
    Elementary duality between left and right modules over a ring, especially its interpretation in terms of the relevant functor categories, is discussed, as is the relationship between these categories of functors and sorts in theories of modules. A topology on the set of indecomposable pure-injective modules over a ring is introduced. This topology is dual to the Ziegler topology and may be seen as a generalisation of the Zariski topology.
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  3.  9
    Purity, spectra and localisation.Mike Prest - 2009 - New York: Cambridge University Press.
    The central aim of this book is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories.
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  4.  15
    On the undecidability of some classes of abelian-by-finite groups.Annalisa Marcja, Mike Prest & Carlo Toffalori - 1993 - Annals of Pure and Applied Logic 62 (2):167-173.
    Let G be a finite group. For every formula ø in the language of groups, let K denote the class of groups H such that ø is a normal abelian subgroup of H and the quotient group H;ø is isomorphic to G. We show that if G is nilpotent and its order is not square-free, then there exists a formula ø such that the theory of K is undecidable.
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  5.  22
    The generalised RK-Order, orthogonality and regular types for modules.Mike Prest - 1985 - Journal of Symbolic Logic 50 (1):202-219.
  6.  17
    Model theory of comodules.Septimiu Crivei, Mike Prest & Geert Reynders - 2004 - Journal of Symbolic Logic 69 (1):137-142.
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  7. DOSEN, K., Rudimentary Kripke models for the intuitionistic propositional calculus EVANS, DM and HRUSHOVSKI, E., On the automorphism groups of finite covers.H. Friedman, Sg Simpson, X. Yu, Mc Laskowski, Ad Greif, A. Marcia, M. Prest, C. Toffalori, A. Pillay & B. Hart - 1993 - Annals of Pure and Applied Logic 62:295.
  8.  14
    Four concepts from "geometrical" stability theory in modules.T. G. Kucera & M. Prest - 1992 - Journal of Symbolic Logic 57 (2):724-740.
  9.  23
    Classification theory for abelian groups with an endomorphism.Annalisa Marcja, Mike Prest & Carlo Toffalori - 1991 - Archive for Mathematical Logic 31 (2):95-104.
  10.  29
    Some Model Theory of Sheaves of Modules.Mike Prest, Vera Puninskaya & Alexandra Ralph - 2004 - Journal of Symbolic Logic 69 (4):1187 - 1199.
    We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related to acyclicity.
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  11.  8
    Interpreting modules in modules.Mike Prest - 1997 - Annals of Pure and Applied Logic 88 (2-3):193-215.
    Rings which, from the ring-theoretic point of view, are very different may well have categories of modules which are extremely similar. More generally, the category of modules over a ring may contain many other categories of modules. Ideas from model theory are of use in elucidating this state of affairs. In particular we investigate the model-theoretic effect of tilting functors between categories of modules.
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  12.  38
    Modules with few types over some finite-dimensional algebras.Mike Prest & Vera Puninskaya - 2002 - Journal of Symbolic Logic 67 (2):841-858.
    Using the description of the Ziegler spectrum we characterise modules with various stability-theoretic properties (ω-stability, superstability, categoricity) over certain classes of finite-dimensional algebras. We also show that, for modules over the algebras we consider, having few types is equivalent to being ω-stable.
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  13.  21
    Tensor product and theories of modules.Mike Prest - 1999 - Journal of Symbolic Logic 64 (2):617-628.
  14.  17
    The representation theories of elementarily equivalent rings.Mike Prest - 1998 - Journal of Symbolic Logic 63 (2):439-450.
  15.  30
    Pure-injectivity and model theory for G-sets.Ravi Rajani & Mike Prest - 2009 - Journal of Symbolic Logic 74 (2):474-488.
    In the model theory of modules the Ziegler spectrum, the space of indecomposable pure-injective modules, has played a key role. We investigate the possibility of defining a similar space in the context of G-sets where G is a group.
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