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Compactness in Infinitary Gödel Logics

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Logic, Language, Information, and Computation (WoLLIC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9803))

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Abstract

We outline some model-building procedures for infinitary Gödel logics, including a suitable ultrapower construction. As an application, we provide two proofs of the fact that the usual characterizations of cardinals \(\kappa \) such that the Compactness and Weak Compactness Theorems hold for the infinitary language \(\mathcal {L}_{\kappa , \kappa }\) are also valid for the corresponding Gödel logics.

Partially supported by FWF grants P-26976-N25, I-1897-N25, I-2671-N35, and W1255-N23.

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Notes

  1. 1.

    Recall that a (proper) filter \(U\ne \wp (X)\) on a set X is a collection of subsets of X that is closed under binary intersections and supersets.

  2. 2.

    As unfortunate as it is, ‘V’ is the usual notation for this.

References

  1. Baaz, M., Preining, N., Zach, R.: First-order Gödel logics. Ann. Pure Appl. Logic 147, 23–47 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Yaacov, I.B., Berenstein, A., Henson, C.W., Usvyatsov, A.: Model theory for metric structures. In: Lecture Notes Series of the London Mathematical Society, vol. 350, pp. 315–427 (2008)

    Google Scholar 

  3. Hanf, W.P.: On a problem of Erdös and Tarski. Fundamenta Mathematicae 53, 325–334 (1964)

    MathSciNet  MATH  Google Scholar 

  4. Jech, T.: Set Theory. Springer, New York (2003)

    MATH  Google Scholar 

  5. Kanamori, A.: The Higher Infinite. Springer, New York (2009)

    MATH  Google Scholar 

  6. Keisler, H.J., Tarski, A.: From accessible to inaccessible cardinals. Fundamenta Mathematicae 53, 225–308 (1964)

    MathSciNet  MATH  Google Scholar 

  7. Scott, D., Tarski, A.: The sentential calculus with infinitely long expressions. Colloquium Mathematicum 16, 166–170 (1958)

    MathSciNet  MATH  Google Scholar 

  8. Tarski, A.: Remarks on predicate logic with infinitely long expressions. Colloquium Mathematicum 16, 171–176 (1958)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Vienna University of Technology, 1040, Vienna, Austria

    Juan P. Aguilera

Authors
  1. Juan P. Aguilera
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Correspondence to Juan P. Aguilera .

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Editors and Affiliations

  1. Dept of Mathematics & Statistics, Univ of Helsinki Dept of Mathematics & Statistics, Helsinki, Finland

    Jouko Väänänen

  2. Department of Mathematics and Statistics, University of Helsinki , Helsinki, Finland

    Åsa Hirvonen

  3. Centro de Informática , Recife, Pernambuco, Brazil

    Ruy de Queiroz

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Aguilera, J.P. (2016). Compactness in Infinitary Gödel Logics. In: Väänänen, J., Hirvonen, Å., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2016. Lecture Notes in Computer Science(), vol 9803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52921-8_2

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  • DOI: https://doi.org/10.1007/978-3-662-52921-8_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-52920-1

  • Online ISBN: 978-3-662-52921-8

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