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December 2013 Logic in the 1930s: type theory and model theory
Erich H. Reck, Georg Schiemer
Bull. Symbolic Logic 19(4): 433-472 (December 2013). DOI: 10.2178/bsl.1904010

Abstract

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of axiomatic theories in the 1930s, by two proponents of the type-theoretic tradition (Carnap and Tarski) and two proponents of the first-order tradition (Gödel and Hilbert), we argue that, instead, the move from type theory to first-order logic is better understood as a gradual transformation, and further, that the contributions to semantics made in the type-theoretic tradition should be seen as central to the evolution of model theory.

Citation

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Erich H. Reck. Georg Schiemer. "Logic in the 1930s: type theory and model theory." Bull. Symbolic Logic 19 (4) 433 - 472, December 2013. https://doi.org/10.2178/bsl.1904010

Information

Published: December 2013
First available in Project Euclid: 5 January 2014

zbMATH: 1326.03006
MathSciNet: MR3157160
Digital Object Identifier: 10.2178/bsl.1904010

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.19 • No. 4 • December 2013
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