ON FORMALISM FREENESS: IMPLEMENTING GÖDEL'S 1946 PRINCETON BICENTENNIAL LECTURE

ON FORMALISM FREENESS: IMPLEMENTING GÖDEL'S 1946 PRINCETON BICENTENNIAL LECTURE

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...

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Veröffentlicht in:The bulletin of symbolic logic 2013-09, Vol.19 (3), p.351-393
1. Verfasser: KENNEDY, JULIETTE
Format: Artikel
Sprache:eng
Schlagworte:
Definability
Formal systems
Logical theorems
Mathematical formalism
Mathematical logic
Mathematical set theory
Mathematical theorems
Mathematics
Model theory
Semantics
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Zusammenfassung: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.
ISSN:1079-8986
1943-5894
DOI:10.1017/S1079898600010684