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  1. Jon Barwise (1969). Applications of Strict Π11 Predicates to Infinitary Logic. Journal of Symbolic Logic 34 (3):409 - 423.
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  2. Jon Barwise (1969). Infinitary Logic and Admissible Sets. Journal of Symbolic Logic 34 (2):226-252.
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  3. 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 called (...)
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  4. Michael Glanzberg (2001). Supervenience and Infinitary Logic. Noûs 35 (3):419-439.
    The discussion of supervenience is replete with the use of in?nitary logical operations. For instance, one may often ?nd a supervenient property that corresponds to an in?nite collection of supervenience-base properties, and then ask about the in?nite disjunction of all those base properties. This is crucial to a well-known argument of Kim (1984) that supervenience comes nearer to reduction than many non-reductive physicalists suppose. It also appears in recent discussions such as Jackson (1998).
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  5. H. Jerome Keisler & Julia F. Knight (2004). Barwise: Infinitary Logic and Admissible Sets. Bulletin of Symbolic Logic 10 (1):4-36.
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  6. James F. Lynch (1997). Infinitary Logics and Very Sparse Random Graphs. Journal of Symbolic Logic 62 (2):609-623.
    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 the (...)
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  7. David Manley (2009). When Best Theories Go Bad. Philosophy and Phenomenological Research 78 (2):392-405.
    It is common for contemporary metaphysical realists to adopt Quine's criterion of ontological commitment while at the same time repudiating his ontological pragmatism. 2 Drawing heavily from the work of others—especially Joseph Melia and Stephen Yablo—I will argue that the resulting approach to meta-ontology is unstable. In particular, if we are metaphysical realists, we need not accept ontological commitment to whatever is quantified over by our best first-order theories.
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  8. Richard Mansfield (1972). The Completeness Theorem for Infinitary Logic. Journal of Symbolic Logic 37 (1):31-34.
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  9. Slavian Radev (1987). Infinitary Propositional Normal Modal Logic. Studia Logica 46 (4):291 - 309.
    A logic with normal modal operators and countable infinite conjunctions and disjunctions is introduced. A Hilbert's style axiomatization is proved complete for this logic, as well as for countable sublogics and subtheories. It is also shown that the logic has the interpolation property.
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  10. Krister Segerberg (1994). A Model Existence Theorem in Infinitary Propositional Modal Logic. Journal of Philosophical Logic 23 (4):337 - 367.
  11. Saharon Shelah & Jouko Väänänen (2000). Stationary Sets and Infinitary Logic. Journal of Symbolic Logic 65 (3):1311-1320.
    Let K 0 λ be the class of structures $\langle\lambda, , where $A \subseteq \lambda$ is disjoint from a club, and let K 1 λ be the class of structures $\langle\lambda, , where $A \subseteq \lambda$ contains a club. We prove that if $\lambda = \lambda^{ is regular, then no sentence of L λ+κ separates K 0 λ and K 1 λ . On the other hand, we prove that if $\lambda = \mu^+,\mu = \mu^{ , and a forcing axiom (...)
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  12. Kenneth Slonneger (1976). A Complete Infinitary Logic. Journal of Symbolic Logic 41 (4):730-746.
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