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Michael C. Laskowski [26]Michael Chris Laskowski [2]
  1.  9
    Disjoint Amalgamation in Locally Finite Aec.John T. Baldwin, Martin Koerwien & Michael C. Laskowski - 2017 - Journal of Symbolic Logic 82 (1):98-119.
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  2.  58
    On VC-Minimal Theories and Variants.Vincent Guingona & Michael C. Laskowski - 2013 - Archive for Mathematical Logic 52 (7-8):743-758.
    In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VC-minimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full VC-minimality, (...)
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  3.  6
    Henkin Constructions of Models with Size Continuum.John T. Baldwin & Michael C. Laskowski - 2019 - Bulletin of Symbolic Logic 25 (1):1-33.
    We describe techniques for constructing models of size continuum inωsteps by simultaneously building a perfect set of enmeshed countable Henkin sets. Such models have perfect, asymptotically similar subsets. We survey applications involving Borel models, atomic models, two-cardinal transfers and models respecting various closure relations.
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  4.  76
    Model Completeness for Trivial, Uncountably Categorical Theories of Morley Rank 1.Alfred Dolich, Michael C. Laskowski & Alexander Raichev - 2006 - Archive for Mathematical Logic 45 (8):931-945.
    We show that if T is a trivial uncountably categorical theory of Morley Rank 1 then T is model complete after naming constants for a model.
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  5.  76
    Provability in Predicate Product Logic.Michael C. Laskowski & Shirin Malekpour - 2007 - Archive for Mathematical Logic 46 (5-6):365-378.
    We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document}. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi\forall}$$\end{document} if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.
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  6.  22
    Mutually Algebraic Structures and Expansions by Predicates.Michael C. Laskowski - 2013 - Journal of Symbolic Logic 78 (1):185-194.
    We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion $(M,A)$ by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct, and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic (...)
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  7.  22
    Uncountable Theories That Are Categorical in a Higher Power.Michael Chris Laskowski - 1988 - Journal of Symbolic Logic 53 (2):512-530.
    In this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime and minimal models over arbitrary base sets. The second theorem shows that such theories have a natural notion of dimension that determines the models of the theory up to isomorphism. From this we conclude that $I(T, \aleph_\alpha) = \aleph_0 +|\alpha|$ where ℵ α = the number of formulas (...)
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  8.  47
    The Elementary Diagram of a Trivial, Weakly Minimal Structure is Near Model Complete.Michael C. Laskowski - 2009 - Archive for Mathematical Logic 48 (1):15-24.
    We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas.
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  9.  20
    An Old Friend Revisited: Countable Models of Ω-Stable Theories.Michael C. Laskowski - 2007 - Notre Dame Journal of Formal Logic 48 (1):133-141.
    We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.
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  10.  18
    On o-Minimal Expansions of Archimedean Ordered Groups.Michael C. Laskowski & Charles Steinhorn - 1995 - Journal of Symbolic Logic 60 (3):817-831.
    We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion of R. (...)
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  11.  9
    S-Homogeneity and Automorphism Groups.Elisabeth Bouscaren & Michael C. Laskowski - 1993 - Journal of Symbolic Logic 58 (4):1302-1322.
    We consider the question of when, given a subset A of M, the setwise stabilizer of the group of automorphisms induces a closed subgroup on Sym(A). We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that any subset of a countable, s-homogeneous, ω-stable structure induces a closed subgroup and contrast this with a number of negative results. We also show that for ω-stable structures s-homogeneity is preserved under naming countably many constants, but under slightly (...)
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  12.  17
    San Antonio Convention Center San Antonio, Texas January 14–15, 2006.Douglas Cenzer, C. Ward Henson, Michael C. Laskowski, Alain Louveau, Russell Miller, Itay Neeman, Sergei Starchenko & Valentina Harizanov - 2006 - Bulletin of Symbolic Logic 12 (4).
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  13.  6
    Weakly Minimal Groups with a New Predicate.Gabriel Conant & Michael C. Laskowski - 2020 - Journal of Mathematical Logic 20 (2):2050011.
    Fix a weakly minimal (i.e. superstable U-rank 1) structure M. Let M∗ be an expansion by constants for an elementary substructure, and let A be an arbitrary subset of the universe M. We show that all formulas in the expansion (M∗,A) are equivalent to bounded formulas, and so (M,A) is stable (or NIP) if and only if the M-induced structure AM on A is stable (or NIP). We then restrict to the case that M is a pure abelian group with (...)
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  14. Books to Asl, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference. [REVIEW]Mirna Dzamonja, David M. Evans, Erich Grädel, Geoffrey P. Hellman, Denis Hirschfeldt, Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2).
     
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  15. The Bulletin of Symbolic Logic Volume 11, Number 2, June 2005.Mirna Dzamonja, David M. Evans, Erich Gradel, Geoffrey P. Hellman, Denis Hirschfeldt, Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2).
  16.  26
    Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW]David M. Evans, Erich Grädel, Geoffrey P. Hellman, Denis Hirschfeldt, Thomas J. Jech, Julia Knight, Michael C. Laskowski, Volker Peckhaus, Wolfram Pohlers & Sławomir Solecki - 2005 - Bulletin of Symbolic Logic 11 (1):37.
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  17.  17
    Unique Decomposition in Classifiable Theories.Bradd Hart, Ehud Hrushovski & Michael C. Laskowski - 2002 - Journal of Symbolic Logic 67 (1):61-68.
  18.  10
    Books to ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA.Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2004 - Bulletin of Symbolic Logic 10 (3).
  19.  12
    An Application of Kochen's Theorem.Michael C. Laskowski - 2003 - Journal of Symbolic Logic 68 (4):1181-1188.
    We describe the Ax-Kochen definable subsets of the value group of a Hensel field and apply our results to a problem on identifying invariant factors in Hecke algebras.
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  20.  11
    A Strong Failure of $$\aleph _0$$ ℵ 0 -Stability for Atomic Classes.Michael C. Laskowski & Saharon Shelah - 2019 - Archive for Mathematical Logic 58 (1-2):99-118.
    We study classes of atomic models \ of a countable, complete first-order theory T. We prove that if \ is not \-small, i.e., there is an atomic model N that realizes uncountably many types over \\) for some finite \ from N, then there are \ non-isomorphic atomic models of T, each of size \.
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  21.  9
    Characterizing Model Completeness Among Mutually Algebraic Structures.Michael C. Laskowski - 2015 - Notre Dame Journal of Formal Logic 56 (3):463-470.
    We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields a new, more constructive proof that the elementary diagram of any model of a strongly minimal, trivial theory is model complete.
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  22.  4
    Review: Steven Buechler, Essential Stability Theory. [REVIEW]Michael C. Laskowski - 1998 - Journal of Symbolic Logic 63 (1):325-326.
  23.  12
    Steven Buechler. Essential Stability Theory. Perspectives in Mathematical Logic. Springer, Berlin, Heidelberg, New York, Etc., 1996, Xiv + 355 Pp. [REVIEW]Michael C. Laskowski - 1998 - Journal of Symbolic Logic 63 (1):325-326.
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  24.  16
    Stable Structures with Few Substructures.Michael C. Laskowski & Laura L. Mayer - 1996 - Journal of Symbolic Logic 61 (3):985-1005.
    A countable, atomically stable structure U in a finite, relational language has fewer than 2 ω non-isomorphic substructures if and only if U is cellular. An example shows that the finiteness of the language is necessary.
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  25.  9
    Uniformly Bounded Arrays and Mutually Algebraic Structures.Michael C. Laskowski & Caroline A. Terry - 2020 - Notre Dame Journal of Formal Logic 61 (2):265-282.
    We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.
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  26.  12
    The Categoricity Spectrum of Pseudo-Elementary Classes.Michael Chris Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (3):332-347.