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  1. Completeness for Systems Including Real Numbers.W. Balzer & M. Reiter - 1989 - Studia Logica 48 (1):67 - 75.
    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 (...)
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  • Reduction, Representation and Commensurability of Theories.Peter Schroeder-Heister & Frank Schaefer - 1989 - Philosophy of Science 56 (1):130-157.
    Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...)
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