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CARNAP ON EXTREMAL AXIOMS, “COMPLETENESS OF THE MODELS,” AND CATEGORICITY

Published online by Cambridge University Press:  11 July 2012

GEORG SCHIEMER
GEORG SCHIEMER*
Affiliation:
Munich Center for Mathematical Philosophy, Ludwig-Maximilians-University Munich
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITY MUNICH 80539 MUNICH, GERMANY Email:[email protected]
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Abstract

This paper provides a historically sensitive discussion of Carnap’s theory of extremal axioms developed first in the late 1920s. The main focus is set on the unpublished documents of the projected second part of his manuscript Untersuchungen zur allgemeinen Axiomatik (RC 081-01-01 to 081-01-33). Carnap’s theory will be assessed with respect to two interpretive issues. The first concerns his mathematical sources, that is, the mathematical axioms on which his extremal axioms were based. The second concerns Carnap’s understanding of the relationship between the “completeness of the models” and other metatheoretic notions investigated by him at the time, most notably that of categoricity. The paper surveys Carnap’s different attempts to explicate the extremal properties of a theory and puts his results in context with related metamathematical research at the time.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 613 - 641
Copyright
Copyright © Association for Symbolic Logic 2012

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