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  1. Stål Aanderaa & Dag Belsnes (1971). Decision Problems for Tag Systems. Journal of Symbolic Logic 36 (2):229-239.
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  2. Stål Aanderaa & Warren D. Goldfarb (1974). The Finite Controllability of the Maslov Case. Journal of Symbolic Logic 39 (3):509-518.
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  3. S. Kamal Abdali (1976). An Abstraction Algorithm for Combinatory Logic. Journal of Symbolic Logic 41 (1):222-224.
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  4. Alexander Abian (1973). Rado's Theorem and Solvability of Systems of Equations. Notre Dame Journal of Formal Logic 14 (2):145-150.
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  5. Alexander Abian (1970). Completeness of the Generalized Propositional Calculus. Notre Dame Journal of Formal Logic 11 (4):449-452.
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  6. Uri Abraham, James Cummings & Clifford Smyth (2007). Some Results in Polychromatic Ramsey Theory. Journal of Symbolic Logic 72 (3):865 - 896.
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  7. Jarosław Achinger (1986). Generalization of Scott's Formula for Retractions From Generalized Alexandroff's Cube. Studia Logica 45 (3):281 - 292.
    In the paper [2] the following theorem is shown: Theorem (Th. 3,5, [2]), If =0 or = or , then a closure space X is an absolute extensor for the category of , -closure spaces iff a contraction of X is the closure space of all , -filters in an , -semidistributive lattice.In the case when = and =, this theorem becomes Scott's theorem.
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  8. Jarosław Achinger & Andrzej W. Jankowski (1986). On Decidable Consequence Operators. Studia Logica 45 (4):415 - 424.
    The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
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  9. Robert Ackermann (1971). Matrix Satisfiability and Axiomatization. Notre Dame Journal of Formal Logic 12 (3):309-321.
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  10. Jiří Adámek (2004). On Quasivarieties and Varieties as Categories. Studia Logica 78 (1-2):7 - 33.
    Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, –) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.
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  11. Jiří Adámek, Alan H. Mekler, Evelyn Nelson & Jan Reiterman (1988). On the Logic of Continuous Algebras. Notre Dame Journal of Formal Logic 29 (3):365-380.
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  12. Zofia Adamowicz (1991). On Maximal Theories. Journal of Symbolic Logic 56 (3):885-890.
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  13. Zofia Adamowicz (1987). Open Induction and the True Theory of Rationals. Journal of Symbolic Logic 52 (3):793-801.
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  14. Zofia Adamowicz & Guillermo Morales-Luna (1985). A Recursive Model for Arithmetic with Weak Induction. Journal of Symbolic Logic 50 (1):49-54.
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  15. Alan Adamson & Robin Giles (1979). A Game-Based Formal System for Ł∞. Studia Logica 38 (1):49-73.
    A formal system for , based on a game-theoretic analysis of the ukasiewicz prepositional connectives, is defined and proved to be complete. An Herbrand theorem for the predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.
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  16. Hans Adler (2009). A Geometric Introduction to Forking and Thorn-Forking. Journal of Mathematical Logic 9 (01):1-20.
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  17. Hans Adler (2009). Thorn-Forking as Local Forking. Journal of Mathematical Logic 9 (01):21-38.
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  18. Mojtaba Aghaei & Mohammad Ardeshir (2001). Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic. Studia Logica 68 (2):263-285.
    We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.
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  19. P. Aglianò, I. M. A. Ferreirim & F. Montagna (2007). Basic Hoops: An Algebraic Study of Continuous T -Norms. Studia Logica 87 (1):73 - 98.
    A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...)
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  20. Thomas Ågotnes, Wiebe van der Hoek & Michael Wooldridge (2008). Quantified Coalition Logic. Synthese 165 (2):269 - 294.
    We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is (...)
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  21. I. Aguzarov, R. E. Farey & J. B. Goode (1991). An Infinite Superstable Group has Infinitely Many Conjugacy Classes. Journal of Symbolic Logic 56 (2):618-623.
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  22. Seema Ahmad (1991). Embedding the Diamond in the Σ2 Enumeration Degree. Journal of Symbolic Logic 56 (1):195 - 212.
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  23. Tarek Sayed Ahmed (2005). On Amalgamation in Algebras of Logic. Studia Logica 81 (1):61 - 77.
    We show that not all epimorphisms are surjective in certain classes of infinite dimensional cylindric algebras, Pinter's substitution algebras and Halmos' quasipolyadic algebras with and without equality. It follows that these classes fail to have the strong amalgamation property. This answers a question in [3] and a question of Pigozzi in his landmark paper on amalgamation [9]. The cylindric case was first proved by Judit Madarasz [7]. The proof presented herein is substantially different. By a result of Németi, our result (...)
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  24. Tarek Sayed Ahmed (2002). Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic. Studia Logica 72 (2):285 - 309.
    We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin''s axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey''s omitting types theorem fails for L n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L n has been recently (and quite extensively) studied as a (...)
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  25. Miklos Ajtai & Ronald Fagin (1990). Reachability is Harder for Directed Than for Undirected Finite Graphs. Journal of Symbolic Logic 55 (1):113-150.
    Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic second-order sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain "built-in" relations, such as the successor relation). The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence.
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  26. Ryota Akiyoshi (2010). Tait's Conservative Extension Theorem Revisited. Journal of Symbolic Logic 75 (1):155-167.
    This paper aims to give a correct proof of Tait's conservative extension theorem. Tait's own proof is flawed in the sense that there are some invalid steps in his argument, and there is a counterexample to the main theorem from which the conservative extension theorem is supposed to follow. However, an analysis of Tait's basic idea suggests a correct proof of the conservative extension theorem and a corrected version of the main theorem.
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  27. Douglas Albert, Robert Baldinger & John Rhodes (1992). Undecidability of the Identity Problem for Finite Semigroups. Journal of Symbolic Logic 57 (1):179-192.
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  28. Michael H. Albert (1987). A Preservation Theorem for EC-Structures with Applications. Journal of Symbolic Logic 52 (3):779-785.
    We characterize the model companions of universal Horn classes generated by a two-element algebra (or ordered two-element algebra). We begin by proving that given two mutually model consistent classes M and N of L (respectively L') structures, with $\mathscr{L} \subseteq \mathscr{L}'$ , M ec = N ec ∣ L , provided that an L-definability condition for the function and relation symbols of L' holds. We use this, together with Post's characterization of ISP(A), where A is a two-element algebra, to show (...)
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  29. Michael H. Albert & Ross Willard (1987). Injectives in Finitely Generated Universal Horn Classes. Journal of Symbolic Logic 52 (3):786-792.
    Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is injective in ISP(K). We use this result to establish that A is injective in ISP(A) for every two-element algebra A.
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  30. Luca Alberucci & Alessandro Facchini (2009). On Modal Μ -Calculus and Gödel-Löb Logic. Studia Logica 91 (2):145 - 169.
    We show that the modal µ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal µ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the (...)
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  31. Natasha Alechina & Michiel van Lambalgen (1996). Generalized Quantification as Substructural Logic. Journal of Symbolic Logic 61 (3):1006-1044.
    We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of (...)
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  32. Michael Alekhnovich, Sam Buss, Shlomo Moran & Toniann Pitassi (2001). Minimum Propositional Proof Length is NP-Hard to Linearly Approximate. Journal of Symbolic Logic 66 (1):171-191.
    We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by (...)
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  33. Samuel Alexander (forthcoming). Guessing, Mind-Changing, and the Second Ambiguous Class. Notre Dame Journal of Formal Logic.
    In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the second ambiguous class (boldface Delta^0_2), iff it is eventually annihilated by a certain remainder. We simplify this remainder and give a new proof of the latter equivalence. We then introduce a notion of guessing with an ordinal limit on how often one can change one's mind. We show that for (...)
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  34. Samuel Alexander (2013). The First-Order Syntax of Variadic Functions. Notre Dame Journal of Formal Logic 54 (1):47-59.
    We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
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  35. Christopher P. Alfeld (2008). Classifying the Branching Degrees in the Medvedev Lattice of $\Pi^0_1$ Classes. Notre Dame Journal of Formal Logic 49 (3):227-243.
    A $\Pi^0_1$ class can be defined as the set of infinite paths through a computable tree. For classes $P$ and $Q$, say that $P$ is Medvedev reducible to $Q$, $P \leq_M Q$, if there is a computably continuous functional mapping $Q$ into $P$. Let $\mathcal{L}_M$ be the lattice of degrees formed by $\Pi^0_1$ subclasses of $2^\omega$ under the Medvedev reducibility. In "Non-branching degrees in the Medvedev lattice of $\Pi \sp{0}\sb{1} classes," I provided a characterization of nonbranching/branching and a classification of (...)
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  36. Christopher P. Alfeld (2007). Non-Branching Degrees in the Medvedev Lattice of [Image] Classes. Journal of Symbolic Logic 72 (1):81 - 97.
    A $\Pi _{1}^{0}$ class is the set of paths through a computable tree. Given classes P and Q, P is Medvedev reducible to Q, P ≤M Q, if there is a computably continuous functional mapping Q into P. We look at the lattice formed by $\Pi _{1}^{0}$ subclasses of 2ω under this reduction. It is known that the degree of a splitting class of c.e. sets is non-branching. We further characterize non-branching degrees, providing two additional properties which guarantee non-branching: inseparable (...)
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  37. Gerard Allwein & Wendy MacCaull (2001). A Kripke Semantics for the Logic of Gelfand Quantales. Studia Logica 68 (2):173-228.
    Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for (...)
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  38. Teresa Almada & JÚlia Vaz de Carvalho (2001). A Generalization of the Łukasiewicz Algebras. Studia Logica 69 (3):329-338.
    We introduce the variety n m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety n m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety n m contains the variety of ukasiewicz algebras of order n.
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  39. Agostinho Almeida (2009). Canonical Extensions and Relational Representations of Lattices with Negation. Studia Logica 91 (2):171 - 199.
    This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation or (...)
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  40. Ahmad Almukdad & David Nelson (1984). Constructible Falsity and Inexact Predicates. Journal of Symbolic Logic 49 (1):231-233.
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  41. Tuna Altinel & Gregory Cherlin (1999). On Central Extensions of Algebraic Groups. Journal of Symbolic Logic 64 (1):68-74.
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  42. Andris Ambainis, John Case, Sanjay Jain & Mandayam Suraj (2004). Parsimony Hierarchies for Inductive Inference. Journal of Symbolic Logic 69 (1):287-327.
    Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. (...)
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  43. Olga Ambas (2001). Anshakov-Rychkov Algebras. Notre Dame Journal of Formal Logic 42 (4):211-224.
    The aim of this paper is to show that the calculi described by Anshakov and Rychkov are algebraizable in the sense of Blok and Pigozzi. As a consequence, a proof of the strong completeness of these calculi is obtained.
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  44. K. Ambos-Spies & M. Lerman (1989). Lattice Embeddings Into the Recursively Enumerable Degrees. II. Journal of Symbolic Logic 54 (3):735-760.
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  45. K. Ambos-Spies & M. Lerman (1986). Lattice Embeddings Into the Recursively Enumerable Degrees. Journal of Symbolic Logic 51 (2):257-272.
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  46. Klaus Ambos-Spies (1984). An Extension of the Nondiamond Theorem in Classical and Α-Recursion Theory. Journal of Symbolic Logic 49 (2):586-607.
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  47. Klaus Ambos-Spies, Decheng Ding, Wei Wang & Liang Yu (2009). Bounding Non- GL ₂ and R.E.A. Journal of Symbolic Logic 74 (3):989-1000.
    We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.
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  48. Klaus Ambos-Spies & Peter A. Fejer (1988). Degree Theoretical Splitting Properties of Recursively Enumerable Sets. Journal of Symbolic Logic 53 (4):1110-1137.
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  49. Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp & Manuel Lerman (1996). Decidability of the Two-Quantifier Theory of the Recursively Enumerable Weak Truth-Table Degrees and Other Distributive Upper Semi-Lattices. Journal of Symbolic Logic 61 (3):880-905.
    We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...)
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  50. Klaus Ambos-Spies, Bj�Rn Kjos-Hanssen, Steffen Lempp & Theodore A. Slaman (2004). Comparing DNR and WWKL. Journal of Symbolic Logic 69 (4):1089 - 1104.
    In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally nonrecursive functions, is strictly weaker than WWKL₀ (weak weak König's Lemma).
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