Self-referential theories
Logic
2020-08-27 v1
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.
Cite
@article{arxiv.2008.11535,
title = {Self-referential theories},
author = {Samuel Allen Alexander},
journal= {arXiv preprint arXiv:2008.11535},
year = {2020}
}
Comments
25 pages. Accepted for publication in the Journal of Symbolic Logic