Self-referential theories

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.

25 pages. Accepted for publication in the Journal of Symbolic Logic

References in corpus (1)

• A machine that knows its own code