26 found
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  1.  9
    The Logic of Provability.Philip Scowcroft & George Boolos - 1995 - Philosophical Review 104 (4):627.
    This is a book that every enthusiast for Gödel’s proofs of his incompleteness theorems will want to own. It gives an up-to-date account of connections between systems of modal logic and results on provability in formal systems for arithmetic, analysis, and set theory.
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  2.  12
    Corrigendum to “Model-Completions for Abelian Lattice-Ordered Groups with Finitely Many Disjoint Elements” [Ann. Pure Appl. Logic 170 673–698]. [REVIEW]Philip Scowcroft - 2019 - Annals of Pure and Applied Logic 170 (11):102720.
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  3.  26
    On the Structure of Semialgebraic Sets Over P-Adic Fields.Philip Scowcroft & Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (4):1138-1164.
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  4.  31
    Daniel Lascar. Stabilité En Théorie des Modèles. French Original of the Preceding. Monographies de Mathèmatique, No. 2. Institut de Mathématique Pure Et Appliquée, Université Catholique de Louvain, Louvain-la-Neuve1986, 231 Pp. - Ray Mines, Fred Richman, and Wim Ruitenburg. A Course in Constructive Algebra. Universitext. Springer-Verlag, New York, Berlin, Heidelberg, Etc., 1988, Xi + 344 Pp. [REVIEW]Philip Scowcroft - 1990 - Journal of Symbolic Logic 55 (2):883-886.
  5.  36
    2011–2012 Winter Meeting of the Association for Symbolic Logic, John B. Hynes Veterans Memorial Convention Center, Boston Marriott Hotel, and Boston Sheraton Hotel, Boston, MA, January 6–7, 2012. [REVIEW]Philip Scowcroft - 2013 - Bulletin of Symbolic Logic 19 (2):223-235.
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  6.  9
    Model-Completions for Abelian Lattice-Ordered Groups with Finitely Many Disjoint Elements.Philip Scowcroft - 2019 - Annals of Pure and Applied Logic 170 (6):673-698.
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  7.  11
    The Real-Algebraic Structure of Scott's Model of Intuitionistic Analysis.Philip Scowcroft - 1984 - Annals of Pure and Applied Logic 27 (3):275-308.
  8.  4
    A New Model for Intuitionistic Analysis.Philip Scowcroft - 1990 - Annals of Pure and Applied Logic 47 (2):145-165.
  9.  8
    More on Real Algebra in Scott's Model.Philip Scowcroft - 1986 - Annals of Pure and Applied Logic 30 (3):277-291.
  10.  3
    A Transfer Theorem in Constructive Real Algebra.Philip Scowcroft - 1988 - Annals of Pure and Applied Logic 40 (1):29-87.
  11.  7
    Some Model-Theoretic Correspondences Between Dimension Groups and AF Algebras.Philip Scowcroft - 2011 - Annals of Pure and Applied Logic 162 (9):755-785.
    If are structures for a first-order language , is said to be algebraically closed in just in case every positive existential -sentence true in is true in . In 1976 Elliott showed that unital AF algebras are classified up to isomorphism by corresponding dimension groups with order unit. This paper shows that one dimension group with order unit is algebraically closed in another just in case the corresponding AF algebras, viewed as metric structures, fall in the same relation.
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  12.  13
    On the Elimination of Imaginaries From Certain Valued Fields.Philip Scowcroft & Angus Macintyre - 1993 - Annals of Pure and Applied Logic 61 (3):241-276.
    A nontrivial ring with unit eliminates imaginaries just in case its complete theory has the following property: every definable m-ary equivalence relation E may be defined by a formula f = f, where f is an m-ary definable function. We show that for certain natural expansions of the field of p-adic numbers, elimination of imaginaries fails or is independent of ZPC. Similar results hold for certain fields of formal power series.
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  13.  1
    Generalized Halfspaces in Dimension Groups.Philip Scowcroft - 2008 - Annals of Pure and Applied Logic 154 (1):8-26.
    In a dimension group, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The dimension groups obeying a stronger version of this result, true in dense Archimedean ordered groups, are characterized algebraically and provided with a simple set of axioms.
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  14.  23
    More on Definable Sets of P-Adic Numbers.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):912-920.
  15.  18
    A Note on Definable Skolem Functions.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):905-911.
  16.  11
    Some Purely Topological Models for Intuitionistic Analysis.Philip Scowcroft - 1999 - Annals of Pure and Applied Logic 98 (1-3):173-215.
    If one builds a topological model, analogous to that of Moschovakis , over the product of uncountably many copies of the Cantor set, one obtains a structure elementarily equivalent to Krol's model . In an intuitionistic metatheory Moschovakis's original model satisfies all the axioms of intuitionistic analysis, including the unrestricted version of weak continuity for numbers.
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  17.  23
    More on Brouwer's Refutations.Philip Scowcroft - 1989 - Annals of Pure and Applied Logic 41 (1):83-91.
  18.  5
    L -Groups C in Continuous Logic.Philip Scowcroft - 2018 - Archive for Mathematical Logic 57 (3-4):239-272.
    In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive formulas (...)
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  19.  12
    Review: Daniel Lascar, Stabilite En Theorie des Modeles; Ray Mines, Fred Richman, Wim Ruitenburg, A Course in Constructive Algebra. [REVIEW]Philip Scowcroft - 1990 - Journal of Symbolic Logic 55 (2):883-886.
  20.  7
    More on Imaginaries in $P$-Adic Fields.Philip Scowcroft - 1997 - Journal of Symbolic Logic 62 (1):1-13.
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  21.  8
    More on Generic Dimension Groups.Philip Scowcroft - 2015 - Notre Dame Journal of Formal Logic 56 (4):511-553.
    While finitely generic dimension groups are known to admit no proper self-embeddings, these groups also have no automorphisms other than scalar multiplications, and every countable infinitely generic dimension group admits proper self-embeddings and has automorphisms other than scalar multiplications. The finite-forcing companion of the theory of dimension groups is recursively isomorphic to first-order arithmetic, the infinite-forcing companion of the theory of dimension groups is recursively isomorphic to second-order arithmetic, and the first-order theory of existentially closed dimension groups is a complete (...)
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  22.  8
    Generalized Halfspaces in the Mixed-Integer Realm.Philip Scowcroft - 2009 - Notre Dame Journal of Formal Logic 50 (1):43-51.
    In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.
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  23.  15
    More on Imaginaries in P-Adic Fields.Philip Scowcroft - 1997 - Journal of Symbolic Logic 62 (1):1-13.
  24.  6
    Erratum to “Elimination of Unbounded Quantifiers for Some Poly-Regular Groups of Infinite Rank” [Ann. Pure Appl. Logic 149 (1–3) (2007) 40–80]. [REVIEW]Philip Scowcroft - 2013 - Annals of Pure and Applied Logic 164 (1):65.
  25.  4
    The Complexity of Bounded Quantifiers in Some Ordered Abelian Groups.Philip Scowcroft - 2007 - Notre Dame Journal of Formal Logic 48 (4):521-550.
    This paper obtains lower and upper bounds for the number of alternations of bounded quantifiers needed to express all formulas in certain ordered Abelian groups admitting elimination of unbounded quantifiers. The paper also establishes model-theoretic tests for equivalence to a formula with a given number of alternations of bounded quantifiers.
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  26.  2
    Elimination of Unbounded Quantifiers for Some Poly-Regular Groups of Infinite Rank.Philip Scowcroft - 2007 - Annals of Pure and Applied Logic 149 (1):40-80.
    This paper extends theorems of Belegradek about poly-regular groups of finite rank to certain poly-regular groups of infinite rank. A model-theoretic property aiding these investigations is the elimination of unbounded quantifiers, and the paper establishes both a general model-theoretic test for this property and results about bounded quantifiers in the special context of ordered Abelian groups.
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