Self-referential theories

Journal of Symbolic Logic 85 (4):1687-1716 (2020)
  Copy   BIBTEX

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.

Author's Profile

Samuel Allen Alexander
Ohio State University (PhD)

Analytics

Added to PP
2020-08-11

Downloads
473 (#36,194)

6 months
126 (#30,179)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?