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

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  1. M. A. Dickmann (1975). Large Infinitary Languages: Model Theory. American Elsevier Pub. Co..score: 150.0
     
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  2. M. A. Dickmann (1970). Model Theory of Infinitary Languages. [Aarhus, Denmark,Universitet, Matematisk Institut].score: 150.0
     
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  3. Herman Ruge Jervell (1972). Herbrand and Skolem Theorems in Infinitary Languages. Oslo,Universitetet I Oslo, Matematisk Institutt.score: 150.0
     
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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.score: 150.0
     
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  5. John Bell, Infinitary Languages.score: 120.0
    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. Kenneth Kunen (1968). Implicit Definability and Infinitary Languages. Journal of Symbolic Logic 33 (3):446-451.score: 90.0
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  7. John Gregory (1974). Beth Definability in Infinitary Languages. Journal of Symbolic Logic 39 (1):22-26.score: 90.0
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  8. 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.score: 90.0
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  9. Jaakko Hintikka & Veikko Rantala (1976). A New Approach to Infinitary Languages. Annals of Mathematical Logic 10 (1):95-115.score: 90.0
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  10. Jean‐Pierre Calais (1972). Partial Isomorphisms and Infinitary Languages. Mathematical Logic Quarterly 18 (25‐30):435-456.score: 90.0
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  11. Karl‐Heinz Diener (1983). On Constructing Infinitary Languages Lα Β Without the Axiom of Choice. Mathematical Logic Quarterly 29 (6):357-376.score: 90.0
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  12. Jörg Flum (1971). A Remark on Infinitary Languages. Journal of Symbolic Logic 36 (3):461-462.score: 90.0
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  13. Anders M. Nyberg (1976). Uniform Inductive Definability and Infinitary Languages. Journal of Symbolic Logic 41 (1):109-120.score: 90.0
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  14. Carol Wood (1972). Forcing for Infinitary Languages. Mathematical Logic Quarterly 18 (25‐30):385-402.score: 90.0
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  15. Jon Barwise (1968). Implicit Definability and Compactness in Infinitary Languages. Lecture Notes in Mathematics 72:1--35.score: 90.0
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  16. C. C. Chang (1972). Review: Jorg Flum, A Remark on Infinitary Languages. [REVIEW] Journal of Symbolic Logic 37 (4):764-764.score: 90.0
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  17. Newton C. A. da Costa & Charles C. Pinter (1976). Α Logic and Infinitary Languages. Mathematical Logic Quarterly 22 (1):105-112.score: 90.0
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  18. Jorg Flum (1974). Review: Jerome Malitz, Universal Classes in Infinitary Languages. [REVIEW] Journal of Symbolic Logic 39 (2):336-336.score: 90.0
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  19. E. G. K. Lopez-Escobar (1970). Review: Kenneth Kunen, Implicit Definability and Infinitary Languages. [REVIEW] Journal of Symbolic Logic 35 (2):341-342.score: 90.0
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  20. Mihaly Makkai (1972). Review: Jon Barwise, Implicit Definability and Compactness in Infinitary Languages. [REVIEW] Journal of Symbolic Logic 37 (1):201-202.score: 90.0
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  21. Michael Makkai (1978). Review: M. A. Dickmann, Large Infinitary Languages. Model Theory. [REVIEW] Journal of Symbolic Logic 43 (1):144-145.score: 90.0
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  22. Gonzalo E. Reyes (1972). Lω₁Ω is Enough: A Reduction Theorem for Some Infinitary Languages. Journal of Symbolic Logic 37 (4):705-710.score: 90.0
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  23. Gonzalo E. Reyes (1972). $L{Omega1omega}$ is Enough: A Reduction Theorem for Some Infinitary Languages. Journal of Symbolic Logic 37 (4):705-710.score: 90.0
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  24. Alexandre Martins Rodrigues & Edelcio de Souza (2011). Model Theoretical Generalization of Steinitz's Theorem. Principia 15 (1):107-110.score: 90.0
    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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  25. Saharon Shelah (1973). Weak Definability in Infinitary Languages. Journal of Symbolic Logic 38 (3):399-404.score: 90.0
    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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  26. Tapani Hyttinen (1991). Preservation by Homomorphisms and Infinitary Languages. Notre Dame Journal of Formal Logic 32 (2):167-172.score: 90.0
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  27. H. Jerome Keisler (1971). Model Theory for Infinitary Logic. Amsterdam,North-Holland Pub. Co..score: 78.0
    Provability, Computability and Reflection.
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  28. Julia F. Knight (1982). Review: J.-P. Ressayre, Boolean Models and Infinitary First Order Languages. [REVIEW] Journal of Symbolic Logic 47 (2):439-439.score: 72.0
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  29. J. -P. Ressayre (1973). Boolean Models and Infinitary First Order Languages. Annals of Mathematical Logic 6 (1):41-92.score: 72.0
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  30. John T. Baldwin (2007). The Vaught Conjecture: Do Uncountable Models Count? Notre Dame Journal of Formal Logic 48 (1):79-92.score: 60.0
    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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  31. Karl‐Heinz Diener & K.‐H. Diener (1992). On the Transitive Hull of a Κ‐Narrow Relation. Mathematical Logic Quarterly 38 (1):387-398.score: 60.0
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  32. Victor Pambuccian (2002). On Definitions in an Infinitary Language. Mathematical Logic Quarterly 48 (4):522-524.score: 60.0
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  33. Matti Linna (1970). The Set of Schemata of C-Valid Equations Between Regular Expressions is Independent of the Basic Alphabet. Turku [Finland]Turun Yliopisto.score: 60.0
     
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  34. John L. Bell, Infinitary Logic. Stanford Encyclopedia of Philosophy.score: 48.0
    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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  35. Maaret Karttunen (1983). Model Theoretic Results for Infinitely Deep Languages. Studia Logica 42 (2-3):223 - 241.score: 48.0
    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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  36. E. G. K. Lopez-Escobar (1967). Remarks on an Infinitary Language with Constructive Formulas. Journal of Symbolic Logic 32 (3):305-318.score: 36.0
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  37. Erwin Engeler (1969). Review: E. G. K. Lopez-Escobar, An Interpolation Theorem for Denumerably Long Formulas; E. G. K. Lopez-Escobar, Universal Formulas in the Infinitary Language $L_{Alpha Beta}$. [REVIEW] Journal of Symbolic Logic 34 (2):301-302.score: 36.0
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  38. Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.score: 30.0
    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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  39. Solomon Feferman, What Kind of Logic is “Independence Friendly” Logic?score: 30.0
    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 (1936), (...)
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  40. Miklós Ferenczi (2009). On Conservative Extensions in Logics with Infinitary Predicates. Studia Logica 92 (1):121 - 135.score: 30.0
    If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for (...)
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  41. Johan Van Benthem & Jan Bergstra (1994). Logic of Transition Systems. Journal of Logic, Language and Information 3 (4):247-283.score: 26.0
    Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this (...)
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  42. Johan Benthem & Jan Bergstra (1994). Logic of Transition Systems. Journal of Logic, Language and Information 3 (4):247-283.score: 26.0
    Labeled transition systems are key structures for modeling computation. In this paper, we show how they lend themselves to ordinary logical analysis (without any special new formalisms), by introducing their standard first-order theory. This perspective enables us to raise several basic model-theoretic questions of definability, axiomatization and preservation for various notions of process equivalence found in the computational literature, and answer them using well-known logical techniques (including the Compactness theorem, Saturation and Ehrenfeucht games). Moreover, we consider what happens to this (...)
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  43. Øystein Linnebo & Agustín Rayo (2012). Hierarchies Ontological and Ideological. Mind 121 (482):269 - 308.score: 24.0
    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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  44. James F. Lynch (1997). Infinitary Logics and Very Sparse Random Graphs. Journal of Symbolic Logic 62 (2):609-623.score: 24.0
    Let L ω ∞ω be the infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n) ≪ n -1 satisfies certain simple conditions on its growth rate, then for every σ∈ L ω ∞ω , the probability that σ holds for (...)
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  45. Ian Pratt & Dominik Schoop (2000). Expressivity in Polygonal, Plane Mereotopology. Journal of Symbolic Logic 65 (2):822-838.score: 24.0
    In recent years, there has been renewed interest in the development of formal languages for describing mereological (part-whole) and topological relationships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as `x is connected' or `x is a part of y', and the entities over which their variables range are, accordingly, not points, but regions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This (...)
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  46. Paul Bankston (2011). Base-Free Formulas in the Lattice-Theoretic Study of Compacta. Archive for Mathematical Logic 50 (5-6):531-542.score: 24.0
    The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known (...)
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  47. J. W. Degen (1999). Complete Infinitary Type Logics. Studia Logica 63 (1):85-119.score: 22.0
    For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are . For a fixed , these three versions are, in the order of increasing strength: the local system (), the global system g() (the difference concerns the conditions on eigenvariables) and the -system () (which has anti-selection terms or Hilbertian -terms, and no conditions on eigenvariables). A full cut elimination (...)
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  48. Jouko Väänänen (2008). The Craig Interpolation Theorem in Abstract Model Theory. Synthese 164 (3):401 - 420.score: 20.0
    The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.
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  49. Patrick Blackburn & Jerry Seligman (1995). Hybrid Languages. Journal of Logic, Language and Information 4 (3):251-272.score: 19.0
    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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  50. Tore Langholm (2006). A Descriptive Characterisation of Linear Languages. Journal of Logic, Language and Information 15 (3):233-250.score: 19.0
    Lautemann et al. (1995) gave a descriptive characterisation of the class of context-free languages, showing that a language is context-free iff it is definable as the set of words satisfying some sentence of a particular logic (fragment) over words. The present notes discuss how to specialise this result to the class of linear languages. Somewhat surprisingly, what would seem the most straightforward specialisation actually fails, due to the fact that linear grammars fail to admit a Greibach normal form. (...)
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