Philosophy of Science 56 (1):130-157 (1989)

Abstract
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 are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce
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DOI 10.1086/289476
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References found in this work BETA

Introduction to Logic.PATRICK SUPPES - 1957 - Dover Publications.
Basic Measurement Theory.Patrick Suppes & Joseph Zinnes - 1963 - In D. Luce & Robert Bush (eds.), Handbook of mathematical psychology, Volume I. John Wiley & Sons.. pp. 1-76.
Introduction to Logic.J. Dopp - 1957 - Journal of Symbolic Logic 22 (4):353-354.
Second-Order Languages and Mathematical Practice.Stewart Shapiro - 1985 - Journal of Symbolic Logic 50 (3):714-742.

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Intertheory Relations From Unified Theories.Gebhard Geiger - 1991 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 22 (2):263-282.

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