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On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture

Published online by Cambridge University Press:  05 September 2014

Juliette Kennedy
Juliette Kennedy*
Affiliation:
Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin Katu 2B), FI-00014, University of Helsinki, Finland, E-mail: juliette.kennedy@helsinki.fi
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Abstract

In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the 20th century.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 19 , Issue 3 , September 2013 , pp. 351 - 393
Copyright
Copyright © Association for Symbolic Logic 2013

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