Search results for 'Infinitary languages' (try it on Scholar)

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  1.  3
    M. A. Dickmann (1975). Large Infinitary Languages: Model Theory. American Elsevier Pub. Co..
  2. M. A. Dickmann (1970). Model Theory of Infinitary Languages. [Aarhus, Denmark,Universitet, Matematisk Institut].
     
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  3. Herman Ruge Jervell (1972). Herbrand and Skolem Theorems in Infinitary Languages. Oslo,Universitetet I Oslo, Matematisk Institutt.
     
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  4. Attila Máté (1971). Incompactness in Infinitary Languages with Respect to Boolean-Valued Interpretations. Szeged,University of Szeged Bolyai Mathematical Institute.
     
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  5. John Bell, Infinitary Languages.
    We begin with the following quotation from Karp [1964]: My interest in infinitary logic dates back to a February day in 1956 when I remarked to my thesis supervisor, Professor Leon Henkin, that a particularly vexing problem would be so simple if only I could write a formula which would say x = 0 or x = 1 or x = 2 etc. To my surprise, he replied, "Well, go ahead." Traditionally, expressions in formal systems have been regarded as (...)
     
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  6. Gonzalo E. Reyes (1972). Lω₁Ω is Enough: A Reduction Theorem for Some Infinitary Languages. Journal of Symbolic Logic 37 (4):705-710.
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  7. John Gregory (1974). Beth Definability in Infinitary Languages. Journal of Symbolic Logic 39 (1):22-26.
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  8. Kenneth Kunen (1968). Implicit Definability and Infinitary Languages. Journal of Symbolic Logic 33 (3):446-451.
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  9.  8
    Jaakko Hintikka & Veikko Rantala (1976). A New Approach to Infinitary Languages. Annals of Mathematical Logic 10 (1):95-115.
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  10.  4
    Jean-Pierre Calais (1972). Partial Isomorphisms and Infinitary Languages. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (25-30):435-456.
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  11.  4
    Newton C. A. da Costa & Charles C. Pinter (1976). Α Logic and Infinitary Languages. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):105-112.
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  12.  4
    Carol Wood (1972). Forcing for Infinitary Languages. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (25-30):385-402.
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  13.  6
    Saharon Shelah (1973). Weak Definability in Infinitary Languages. Journal of Symbolic Logic 38 (3):399-404.
    We shall prove that if a model of cardinality κ can be expanded to a model of a sentence ψ of Lλ+,ω by adding a suitable predicate in more than κ ways, then, it has a submodel of power μ which can be expanded to a model of ψ in $> \mu$ ways provided that λ,κ,μ satisfy suitable conditions.
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  14.  7
    Anders M. Nyberg (1976). Uniform Inductive Definability and Infinitary Languages. Journal of Symbolic Logic 41 (1):109-120.
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  15.  4
    Jörg Flum (1971). A Remark on Infinitary Languages. Journal of Symbolic Logic 36 (3):461-462.
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  16.  1
    Carol Wood (1972). Forcing for Infinitary Languages. Mathematical Logic Quarterly 18 (25‐30):385-402.
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  17.  3
    Victor Harnik (1986). Review: David W. Kueker, Lowenheim-Skolem and Interpolation Theorems in Infinitary Languages; K. Jon Barwise, Mostowski's Collapsing Function and the Closed Unbounded Filter; David W. Kueker, Countable Approximations and Lowenheim-Skolem Theorems. [REVIEW] Journal of Symbolic Logic 51 (1):232-234.
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  18.  1
    Jon Barwise (1968). Implicit Definability and Compactness in Infinitary Languages. Lecture Notes in Mathematics 72 (1):1--35.
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  19.  2
    Karl‐Heinz Diener (1983). On Constructing Infinitary Languages Lα Β Without the Axiom of Choice. Mathematical Logic Quarterly 29 (6):357-376.
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  20.  2
    Jean‐Pierre Calais (1972). Partial Isomorphisms and Infinitary Languages. Mathematical Logic Quarterly 18 (25‐30):435-456.
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  21. C. C. Chang (1972). Review: Jorg Flum, A Remark on Infinitary Languages. [REVIEW] Journal of Symbolic Logic 37 (4):764-764.
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  22. Newton C. A. da Costa & Charles C. Pinter (1976). Α Logic and Infinitary Languages. Mathematical Logic Quarterly 22 (1):105-112.
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  23. Jorg Flum (1974). Review: Jerome Malitz, Universal Classes in Infinitary Languages. [REVIEW] Journal of Symbolic Logic 39 (2):336-336.
  24. E. G. K. Lopez-Escobar (1970). Review: Kenneth Kunen, Implicit Definability and Infinitary Languages. [REVIEW] Journal of Symbolic Logic 35 (2):341-342.
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  25. Mihaly Makkai (1972). Review: Jon Barwise, Implicit Definability and Compactness in Infinitary Languages. [REVIEW] Journal of Symbolic Logic 37 (1):201-202.
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  26. Michael Makkai (1978). Review: M. A. Dickmann, Large Infinitary Languages. Model Theory. [REVIEW] Journal of Symbolic Logic 43 (1):144-145.
  27. Gonzalo E. Reyes (1972). $L{Omega1omega}$ is Enough: A Reduction Theorem for Some Infinitary Languages. Journal of Symbolic Logic 37 (4):705-710.
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  28. Alexandre Rodrigues, Ricardo Filho & Edelcio de Souza (2010). Definability in Infinitary Languages and Invariance by Automorphims. Reports on Mathematical Logic:119-133.
     
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  29. Tapani Hyttinen (1991). Preservation by Homomorphisms and Infinitary Languages. Notre Dame Journal of Formal Logic 32 (2):167-172.
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  30.  1
    J. -P. Ressayre (1973). Boolean Models and Infinitary First Order Languages. Annals of Mathematical Logic 6 (1):41-92.
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  31.  1
    Julia F. Knight (1982). Review: J.-P. Ressayre, Boolean Models and Infinitary First Order Languages. [REVIEW] Journal of Symbolic Logic 47 (2):439-439.
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  32.  23
    H. Jerome Keisler (1971). Model Theory for Infinitary Logic. Amsterdam,North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  33.  1
    Alexandre Martins Rodrigues & Edelcio de Souza (2011). Model Theoretical Generalization of Steinitz's Theorem. Principia 15 (1):107-110.
    Infinitary languages are used to prove that any strong isomorphism of substructures of isomorphic structures can be extended to an isomorphism of the structures. If the structures are models of a theory that has quantifier elimination, any isomorphism of substructures is strong. This theorem is a partial generalization of Steinitz’s theorem for algebraically closed fields and has as special case the analogous theorem for differentially closed fields. In this note, we announce results which will be proved elsewhere. DOI: (...)
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  34.  2
    George Weaver & Irena Penev (2005). From Finitary to Infinitary Second‐Order Logic. Mathematical Logic Quarterly 51 (5):499-506.
    A back and forth condition on interpretations for those second-order languages without functional variables whose non-logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second-order languages with an infinite non-logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second-order (...)
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  35.  44
    John L. Bell, Infinitary Logic. Stanford Encyclopedia of Philosophy.
    Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is (...)
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  36.  10
    John T. Baldwin (2007). The Vaught Conjecture: Do Uncountable Models Count? Notre Dame Journal of Formal Logic 48 (1):79-92.
    We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{ω₁,ω}$-types. The following result is new. Theorem: If a first-order theory is a counterexample to the Vaught Conjecture then it has 2\sp ℵ₁ models of cardinality ℵ₁.
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  37.  3
    Karl‐Heinz Diener & K.‐H. Diener (1992). On the Transitive Hull of a Κ‐Narrow Relation. Mathematical Logic Quarterly 38 (1):387-398.
    We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every infinite cardinal (...)
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  38.  6
    Maaret Karttunen (1983). Model Theoretic Results for Infinitely Deep Languages. Studia Logica 42 (2-3):223 - 241.
    We define a subhierarchy of the infinitely deep languagesN described by Jaakko Hintikka and Veikko Rantala. We shall show that some model theoretic results well-known in the model theory of the ordinary infinitary languages can be generalized for these new languages. Among these are the downward Löwenheim-Skolem and o's theorems as well as some compactness properties.
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  39. Matti Linna (1970). The Set of Schemata of C-Valid Equations Between Regular Expressions is Independent of the Basic Alphabet. Turku [Finland]Turun Yliopisto.
     
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  40.  48
    Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.
    If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal (...)
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  41.  24
    Solomon Feferman, What Kind of Logic is “Independence Friendly” Logic?
    1. Two kinds of logic. To a first approximation there are two main kinds of pursuit in logic. The first is the traditional one going back two millennia, concerned with characterizing the logically valid inferences. The second is the one that emerged most systematically only in the twentieth century, concerned with the semantics of logical operations. In the view of modern, model-theoretical eyes, the first requires the second, but not vice-versa. According to Tarski’s generally accepted account of logical consequence, inference (...)
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  42. Øystein Linnebo & Agustín Rayo (2012). Hierarchies Ontological and Ideological. Mind 121 (482):269 - 308.
    Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.
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  43.  16
    M. J. Cresswell (1973). Logics and Languages. London,Methuen [Distributed in the U.S.A. By Harper & Row.
    Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show (...)
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  44.  18
    Patrick Blackburn & Jerry Seligman (1995). Hybrid Languages. Journal of Logic, Language and Information 4 (3):251-272.
    Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and (...)
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  45. Ralf M. Bader (2012). Supervenience and Infinitary Property-Forming Operations. Philosophical Studies 160 (3):415-423.
    This paper provides an account of the closure conditions that apply to sets of subvening and supervening properties, showing that the criterion that determines under which property-forming operations a particular family of properties is closed is applicable both to the finitary and to the infinitary case. In particular, it will be established that, contra Glanzberg, infinitary operations do not give rise to any additional difficulties beyond those that arise in the finitary case.
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  46.  21
    Marcus Kracht (2011). Interpreted Languages and Compositionality. Springer.
    This book argues that languages are composed of sets of ‘signs’, rather than ‘strings’. This notion, first posited by de Saussure in the early 20th century, has for decades been neglected by linguists, particularly following Chomsky’s heavy critiques of the 1950s. Yet since the emergence of formal semantics in the 1970s, the issue of compositionality has gained traction in the theoretical debate, becoming a selling point for linguistic theories. Yet the concept of ‘compositionality’ itself remains ill-defined, an issue this (...)
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  47.  39
    Olivier Finkel (2008). Topological Complexity of Locally Finite Ω-Languages. Archive for Mathematical Logic 47 (6):625-651.
    Locally finite omega languages were introduced by Ressayre [Formal languages defined by the underlying structure of their words. J Symb Log 53(4):1009–1026, 1988]. These languages are defined by local sentences and extend ω-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite ω-languages are analytic sets, the class LOC ω of locally finite ω-languages meets all finite levels of the Borel hierarchy and there exist (...)
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  48.  21
    Lavinia María Picollo (2013). Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability. Studia Logica 101 (3):601-617.
    Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order (...)
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  49. Xinli Wang (2003). Presuppositional Languages and the Failure of Cross-Language Understanding. Dialogue 42 (01):53-77.
    Why is mutual understanding between two substantially different comprehensive language communities often problematic and even unattainable? To answer this question, the author first introduces a notion of presuppositional languages. Based on the semantic structure of a presuppositional language, the author identifies a significant condition necessary for effective understanding of a language: the interpreter is able to effectively understand a language only if he/she is able to recognize and comprehend its metaphysical presuppositions. The essential role of the knowledge of metaphysical (...)
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  50.  11
    Marcus Kracht (2013). Are Logical Languages Compositional? Studia Logica 101 (6):1319-1340.
    In this paper I argue that in contrast to natural languages, logical languages typically are not compositional. This does not mean that the meaning of expressions cannot be determined at all using some well-defined set of rules. It only means that the meaning of an expression cannot be determined without looking at its form. If one is serious about the compositionality of a logic, the only possibility I see is to define it via abstraction from a variable free (...)
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