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SELF-REFERENTIAL THEORIES

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  07 September 2020

SAMUEL A. ALEXANDER
SAMUEL A. ALEXANDER*
Affiliation:
DEPARTMENT OF MATHEMATICS THE OHIO STATE UNIVERSITYCOLUMBUS, OH43210, USAE-mail: alexander@math.ohio-state.edu
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Abstract

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

Keywords

quantified modal logicstrong mechanistic thesis

MSC classification

Primary: 03F45: Provability logics and related algebras (e.g., diagonalizable algebras)
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 4 , December 2020 , pp. 1687 - 1716
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Copyright
© The Association for Symbolic Logic 2020

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