Studia Logica

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

Completeness for systems including real numbers

  • W. Balzer
  • M. Reiter


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.


Real Number Mathematical Logic Model Theory Classical Mechanic Formal System 
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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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