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Studia Logica

, Volume 48, Issue 1, pp 67–75 | Cite as

Completeness for systems including real numbers

  • W. Balzer
  • M. Reiter
Article

Abstract

The usual completeness theorem for first-order logic is extended in order to allow for a natural incorporation of real analysis. Essentially, this is achieved by building in the set of real numbers into the structures for the language, and by adjusting other semantical notions accordingly. We use many-sorted languages so that the resulting formal systems are general enough for axiomatic treatments of empirical theories without recourse to elements of set theory which are difficult to interprete empirically. Thus we provide a way of applying model theory to empirical theories without “tricky” detours. Our frame is applied to axiomatizations of three empirical theories: classical mechanics, phenomenological thermodynamics, and exchange economics.

Keywords

Real Number Mathematical Logic Model Theory Classical Mechanic Formal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    W. Balzer, C. U. Moulines and J. D. Sneed, An Architectonic for Science, Dordrecht 1987.Google Scholar
  2. [2]
    W. Balzer, Incommensurability, reduction, and translation, Erkenntnis 23 (1985), pp. 255–67.Google Scholar
  3. [3]
    S. Feferman, Two notes on abstract model theory, Part 1, Fundamenta Mathematicae 82 (1974), pp. 153–65.Google Scholar
  4. [4]
    H. Gaifman, Operations on relational structures, functors and classes. I, in: L. Henkin et al. (eds.), Proceedings of the Tarski Symposium, Providence, Rhode Island 1974, pp. 21–39.Google Scholar
  5. [5]
    J. J. McKinsey, A. L. Sugar and P. Suppes, Axiomatic foundations of classical particles mechanics, Journal of Rational Mechanics and Analysis II (1953). pp. 253–72.Google Scholar
  6. [6]
    R. Montague, Deterministic theories, in: R. H. Thomason (ed.), Formal Philosophy: Selected Papers of Richard Montague, Yale UP 1974, pp. 303–63.Google Scholar
  7. [7]
    D. Pearce, Stegmüller on Kuhn and incommensurability, The British Journal for the Philosophy of Science 33 (1982), pp. 389–96.Google Scholar
  8. [8]
    J. R. Shoenfield, Mathematical Logic, Reading Mass. 1967.Google Scholar
  9. [9]
    K. Schuette, Proof Theory, Berlin 1977.Google Scholar
  10. [10]
    W. Stegmüller, The Structure and Dynamics of Theories, Berlin-Heidelberg-New York 1976.Google Scholar
  11. [11]
    H. Weyl, Das Kontinuum, Leipzig 1918.Google Scholar

Copyright information

© Polish Academy of Sciences 1989

Authors and Affiliations

  • W. Balzer
    • 1
  • M. Reiter
    • 1
  1. 1.Seminar Für Philosophie, Logik und Wissenschaftstheorie Universität MünchenDeutschland

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