13 found
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  1.  6
    Non-totally transcendental unidimensional theories.Anand Pillay & Philipp Rothmaler - 1990 - Archive for Mathematical Logic 30 (2):93-111.
  2. Modules with regular generic types. Part IV.Ivo Herzog & Philipp Rothmaler - 1992 - Journal of Symbolic Logic 57 (1):193-199.
  3. When cotorsion modules are pure injective.Ivo Herzog & Philipp Rothmaler - 2009 - Journal of Mathematical Logic 9 (1):63-102.
    We characterize rings over which every cotorsion module is pure injective in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the (...)
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  4.  26
    Some model theory of modules. III. on infiniteness of sets definable in modules.Philipp Rothmaler - 1984 - Journal of Symbolic Logic 49 (1):32-46.
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  5.  6
    Stationary types in moduless.Philipp Rothmaler - 1983 - Mathematical Logic Quarterly 29 (8):445-464.
  6.  5
    Mittag-Leffler modules.Philipp Rothmaler - 1997 - Annals of Pure and Applied Logic 88 (2-3):227-239.
    The main theorem characterizes Mittag-Leffler modules as ‘positively atomic’ modules . This is applied to reduced products of Mittag-Leffler modules and pure-semisimple.
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  7.  20
    A Note onI-Types.Philipp Rothmaler - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (2-6):95-96.
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  8. Strict Mittag-Leffler modules.Pedro Antonio Guil Asensio, M. C. Izurdiaga, Philipp Rothmaler & Blas Torrecillas Jover - 2011 - Mathematical Logic Quarterly 57 (6):566-570.
     
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  9.  9
    Unidimensional modules: uniqueness of maximal non-modular submodels.Anand Pillay & Philipp Rothmaler - 1993 - Annals of Pure and Applied Logic 62 (2):175-181.
    We characterize the non-modular models of a unidimensional first-order theory of modules as the elementary submodels of its prime pure-injective model. We show that in case the maximal non-modular submodel of a given model splits off this is true for every such submodel, and we thus obtain a cancellation result for this situation. Although the theories in question always have models whose maximal non-modular submodel do split off, they may as well have others where they don't. We present a corresponding (...)
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  10.  38
    Some model theory of modules. I. on total transcendence of modules.Philipp Rothmaler - 1983 - Journal of Symbolic Logic 48 (3):570-574.
  11.  22
    Elementary Epimorphisms.Philipp Rothmaler - 2005 - Journal of Symbolic Logic 70 (2):473 - 487.
    The concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).
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  12.  4
    A Note on I‐Types.Philipp Rothmaler - 1981 - Mathematical Logic Quarterly 27 (2‐6):95-96.
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  13.  12
    Some model theory of modules. II. on stability and categoricity of flat modules.Philipp Rothmaler - 1983 - Journal of Symbolic Logic 48 (4):970-985.