English

A note on the consistency operator

Logic 2019-10-29 v3

Abstract

It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory TT, the next strongest natural theory is T+ConTT+\mathsf{Con}_T. We formulate and prove a statement to the effect that the consistency operator is the weakest natural way to uniformly extend axiomatic theories.

Keywords

Cite

@article{arxiv.1905.00998,
  title  = {A note on the consistency operator},
  author = {James Walsh},
  journal= {arXiv preprint arXiv:1905.00998},
  year   = {2019}
}
R2 v1 2026-06-23T08:55:46.827Z