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Andreas Blass [56]Andreas R. Blass [2]
  1.  50
    A game semantics for linear logic.Andreas Blass - 1992 - Annals of Pure and Applied Logic 56 (1-3):183-220.
    We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as the (...)
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  2.  29
    There may be simple Pℵ1 and Pℵ2-points and the Rudin-Keisler ordering may be downward directed.Andreas Blass & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (C):213-243.
  3.  87
    Infinitary combinatorics and modal logic.Andreas Blass - 1990 - Journal of Symbolic Logic 55 (2):761-778.
    We show that the modal propositional logic G, originally introduced to describe the modality "it is provable that", is also sound for various interpretations using filters on ordinal numbers, for example the end-segment filters, the club filters, or the ineffable filters. We also prove that G is complete for the interpretation using end-segment filters. In the case of club filters, we show that G is complete if Jensen's principle □ κ holds for all $\kappa ; on the other hand, it (...)
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  4.  38
    Selective ultrafilters and homogeneity.Andreas Blass - 1988 - Annals of Pure and Applied Logic 38 (3):215-255.
  5.  32
    Near coherence of filters. I. Cofinal equivalence of models of arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
  6.  27
    Near coherence of filters. III. A simplified consistency proof.Andreas Blass & Saharon Shelah - 1989 - Notre Dame Journal of Formal Logic 30 (4):530-538.
  7.  36
    Ramsey's theorem in the hierarchy of choice principles.Andreas Blass - 1977 - Journal of Symbolic Logic 42 (3):387-390.
  8.  68
    When are two algorithms the same?Andreas Blass, Nachum Dershowitz & Yuri Gurevich - 2009 - Bulletin of Symbolic Logic 15 (2):145-168.
    People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.
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  9.  55
    Consistency results about filters and the number of inequivalent growth types.Andreas Blass & Claude Laflamme - 1989 - Journal of Symbolic Logic 54 (1):50-56.
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  10.  44
    Choiceless polynomial time.Andreas Blass, Yuri Gurevich & Saharon Shelah - 1999 - Annals of Pure and Applied Logic 100 (1-3):141-187.
    Turing machines define polynomial time on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time ? Earlier, one of us conjectured a negative answer. The problem motivated a quest for stronger and stronger (...)
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  11.  61
    On the cofinality of ultrapowers.Andreas Blass & Heike Mildenberger - 1999 - Journal of Symbolic Logic 64 (2):727-736.
    We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting number s, the unsplitting number r, and the groupwise density number g. We also prove some related results for reduced powers with respect to filters other than ultrafilters.
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  12.  43
    Groupwise density and related cardinals.Andreas Blass - 1990 - Archive for Mathematical Logic 30 (1):1-11.
    We prove several theorems about the cardinal $\mathfrak{g}$ associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps fromω toω, all families of size $< \mathfrak{g}$ are below all unbounded families. With respect to a natural ordering of filters onω, all filters generated by $< \mathfrak{g}$ sets are below all non-feeble filters. If $\mathfrak{u}< \mathfrak{g}$ then $\mathfrak{b}< \mathfrak{u}$ and $\mathfrak{g} = \mathfrak{d} = \mathfrak{c}$ . (The definitions of these cardinals are recalled in the introduction.) Finally, (...)
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  13.  72
    The logic of choice.Andreas Blass & Yuri Gurevich - 2000 - Journal of Symbolic Logic 65 (3):1264-1310.
    The choice construct (choose x: φ(x)) is useful in software specifications. We study extensions of first-order logic with the choice construct. We prove some results about Hilbert's ε operator, but in the main part of the paper we consider the case when all choices are independent.
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  14.  52
    The intersection of nonstandard models of arithmetic.Andreas Blass - 1972 - Journal of Symbolic Logic 37 (1):103-106.
  15.  57
    The Next Best Thing to a P-Point.Andreas Blass, Natasha Dobrinen & Dilip Raghavan - 2015 - Journal of Symbolic Logic 80 (3):866-900.
    We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but (...)
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  16. On polynomial time computation over unordered structures.Andreas Blass, Yuri Gurevich & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (3):1093-1125.
    This paper is motivated by the question whether there exists a logic capturing polynomial time computation over unordered structures. We consider several algorithmic problems near the border of the known, logically defined complexity classes contained in polynomial time. We show that fixpoint logic plus counting is stronger than might be expected, in that it can express the existence of a complete matching in a bipartite graph. We revisit the known examples that separate polynomial time from fixpoint plus counting. We show (...)
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  17.  72
    On certain types and models for arithmetic.Andreas Blass - 1974 - Journal of Symbolic Logic 39 (1):151-162.
    There is an analogy between concepts such as end-extension types and minimal types in the model theory of Peano arithmetic and concepts such as P-points and selective ultrafilters in the theory of ultrafilters on N. Using the notion of conservative extensions of models, we prove some theorems clarifying the relation between these pairs of analogous concepts. We also use the analogy to obtain some model-theoretic results with techniques originally used in ultrafilter theory. These results assert that every countable nonstandard model (...)
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  18.  57
    The model of set theory generated by countably many generic reals.Andreas Blass - 1981 - Journal of Symbolic Logic 46 (4):732-752.
    Adjoin, to a countable standard model M of Zermelo-Fraenkel set theory (ZF), a countable set A of independent Cohen generic reals. If one attempts to construct the model generated over M by these reals (not necessarily containing A as an element) as the intersection of all standard models that include M ∪ A, the resulting model fails to satisfy the power set axiom, although it does satisfy all the other ZF axioms. Thus, there is no smallest ZF model including M (...)
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  19.  53
    Amalgamation of nonstandard models of arithmetic.Andreas Blass - 1977 - Journal of Symbolic Logic 42 (3):372-386.
    Any two models of arithmetic can be jointly embedded in a third with any prescribed isomorphic submodels as intersection and any prescribed relative ordering of the skies above the intersection. Corollaries include some known and some new theorems about ultrafilters on the natural numbers, for example that every ultrafilter with the "4 to 3" weak Ramsey partition property is a P-point. We also give examples showing that ultrafilters with the "5 to 4" partition property need not be P-points and that (...)
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  20.  55
    Cores of Π11 sets of reals.Andreas Blass & Douglas Cenzer - 1974 - Journal of Symbolic Logic 39 (4):649 - 654.
  21.  56
    Complete topoi representing models of set theory.Andreas Blass & Andre Scedrov - 1992 - Annals of Pure and Applied Logic 57 (1):1-26.
    By a model of set theory we mean a Boolean-valued model of Zermelo-Fraenkel set theory allowing atoms (ZFA), which contains a copy of the ordinary universe of (two-valued,pure) sets as a transitive subclass; examples include Scott-Solovay Boolean-valued models and their symmetric submodels, as well as Fraenkel-Mostowski permutation models. Any such model M can be regarded as a topos. A logical subtopos E of M is said to represent M if it is complete and its cumulative hierarchy, as defined by Fourman (...)
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  22.  32
    Questions and answers–a category arising in linear logic, complexity theory, and set theory.Andreas Blass - 1995 - In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in linear logic. New York, NY, USA: Cambridge University Press. pp. 222--61.
  23. An induction principle and pigeonhole principles for k-finite sets.Andreas Blass - 1995 - Journal of Symbolic Logic 60 (4):1186-1193.
    We establish a course-of-values induction principle for K-finite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by Bénabou and Loiseau. We also comment on some variants of this pigeonhole principle.
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  24.  28
    New Orleans Marriott and Sheraton New Orleans Hotels New Orleans, LA January 8–9, 2011.Jeremy Avigad, Ulrich W. Kohlenbach, Henry Towsner, Samson Abramsky, Andreas Blass, Larry Moss, Alf Onshuus Nino, Patrick Speissegger, Juris Steprans & Monica VanDieren - 2012 - Bulletin of Symbolic Logic 18 (1).
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  25.  20
    Jagadeesan, Radha, 306 Japaridze, Giorgi, xi.Arnon Avron, Oskar Becker, Johan van Benthem, Andreas Blass, Robert Brandom, L. E. J. Brouwer, Donald Davidson, Michael Dummett & Walter Felscher - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Dordrecht, Netherland: Springer Verlag. pp. 377.
    No categories
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  26.  20
    Gainesville, Florida March 10–13, 2007.Michael Benedikt, Andreas Blass, Natasha Dobrinen, Noam Greenberg, Denis R. Hirschfeldt, Salma Kuhlmann, Hannes Leitgeb, William J. Mitchell & Thomas Wilke - 2007 - Bulletin of Symbolic Logic 13 (3).
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  27.  22
    2003 Annual Meeting of the Association for Symbolic Logic.Andreas Blass - 2004 - Bulletin of Symbolic Logic 10 (1):120-145.
  28.  49
    Acknowledgement of priority.Andreas Blass - 1985 - Journal of Symbolic Logic 50 (3):781.
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  29.  19
    (1 other version)Addendum to “Choiceless polynomial time”.Andreas Blass, Yuri Gurevich & Saharon Shelah - 2001 - Annals of Pure and Applied Logic 112 (1):117.
  30.  35
    Divisibility of dedekind finite sets.David Blair, Andreas Blass & Paul Howard - 2005 - Journal of Mathematical Logic 5 (1):49-85.
    A Dedekind-finite set is said to be divisible by a natural number n if it can be partitioned into pieces of size n. We study several aspects of this notion, as well as the stronger notion of being partitionable into n pieces of equal size. Among our results are that the divisors of a Dedekind-finite set can consistently be any set of natural numbers, that a Dedekind-finite power of 2 cannot be divisible by 3, and that a Dedekind-finite set can (...)
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  31.  22
    Meeting of the Association for Symbolic Logic, East Lansing, Michigan, 1988.Andreas Blass & Jacob Plotkin - 1989 - Journal of Symbolic Logic 54 (2):674-677.
  32.  19
    Meeting of the Association for Symbolic Logic, Chicago, 1985.Andreas Blass, Louise Hay & Peter G. Hinman - 1986 - Journal of Symbolic Logic 51 (2):507-510.
  33.  24
    Needed reals and recursion in generic reals.Andreas Blass - 2001 - Annals of Pure and Applied Logic 109 (1-2):77-88.
    We consider sets of reals that are “adequate” in various senses, for example dominating or unbounded or splitting or non-meager. Call a real x “needed” if every adequate set contains a real in which x is recursive. We characterize the needed reals for numerous senses of “adequate.” We also consider, for various notions of forcing that add reals, the problem of characterizing the ground-model reals that are recursive in generic reals.
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  34.  36
    On the inadequacy of inner models.Andreas Blass - 1972 - Journal of Symbolic Logic 37 (3):569-571.
  35.  28
    Preface.Andreas Blass, Su Gao & Yi Zhang - 2009 - Annals of Pure and Applied Logic 158 (3):155.
  36.  18
    Symbioses between mathematical logic and computer science.Andreas Blass - 2016 - Annals of Pure and Applied Logic 167 (10):868-878.
  37.  32
    Small decidable sheaves.Andreas Blass & Andre Scedrov - 1986 - Journal of Symbolic Logic 51 (3):726-731.
  38.  46
    Some initial segments of the Rudin-Keisler ordering.Andreas Blass - 1981 - Journal of Symbolic Logic 46 (1):147-157.
    A 2-affable ultrafilter has only finitely many predecessors in the Rudin-Keisler ordering of isomorphism classes of ultrafilters over the natural numbers. If the continuum hypothesis is true, then there is an ℵ 1 -sequence of ultrafilters D α such that the strict Rudin-Keisler predecessors of D α are precisely the isomorphs of the D β 's for $\beta.
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  39.  42
    Sperner spaces and first‐order logic.Andreas Blass & Victor Pambuccian - 2003 - Mathematical Logic Quarterly 49 (2):111-114.
    We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ∞ω-axiomatizable. We also axiomatize the first-order theory of this class.
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  40.  32
    There are not exactly five objects.Andreas Blass - 1984 - Journal of Symbolic Logic 49 (2):467-469.
    We exhibit a Horn sentence expressing the statement of the title; the construction generalizes to arbitrary primes in place of five.
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  41.  73
    Theories without countable models.Andreas Blass - 1972 - Journal of Symbolic Logic 37 (3):562-568.
  42. [Omega]-Bibliography of Mathematical Logic.G. H. Müller, Wolfgang Lenski & Andreas R. Blass - 1987
     
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  43.  35
    Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time.Andreas Blass & Yuri Gurevich - 2003 - Journal of Symbolic Logic 68 (1):65-131.
    This paper developed from Shelah’s proof of a zero-one law for the complexity class “choiceless polynomial time,” defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws are inadequate in the case of choiceless polynomial time; they must be replaced by what we call the strong extension axioms. We present an extensive (...)
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  44.  27
    (1 other version)Marcia J. Groszek. Applications of iterated perfect set forcing. Annals of pure and applied logic, vol. 39 , pp. 19– 53. [REVIEW]Andreas Blass - 1990 - Journal of Symbolic Logic 55 (1):360-361.
  45.  20
    (1 other version)Michael Makkai and Robert Paré. Accessible categories: the foundations of categorical model theory. Contemporary mathematics, vol. 104. American Mathematical Society, Providence1989, viii + 176 pp. [REVIEW]Andreas Blass - 1993 - Journal of Symbolic Logic 58 (1):355-357.
  46.  33
    Paul Howard and Jean E. Rubin. Consequences of the axiom of choice, Mathematical Surveys and Monographs, vol. 59. American Mathematical Society, Providence, RI, 1998, viii + 432 pp. [REVIEW]Andreas Blass - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.
  47.  28
    (1 other version)Review: W. Hugh Woodin, A. S. Kechris, D. A. Martin, Y. N. Moschavokis, Ad and the Uniqueness of the Supercompact Measures on $Pomega1 (lambda)$; W. Hugh Woodin, Some Consistency Results in ZFC using AD; Alexander S. Kechris, D. A. Martin, J. R. Steel, Subsets of $aleph1$ Constructible from a Real. [REVIEW]Andreas Blass - 1992 - Journal of Symbolic Logic 57 (1):259-261.
  48.  11
    (1 other version)Review: W. W. Comfort, S. Negrepontis, The Theory of Ultrafilters. [REVIEW]Andreas Blass - 1976 - Journal of Symbolic Logic 41 (4):782-783.