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arXiv · 1905.00998

A note on the consistency operator

James Walsh
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Abstract

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

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James Walsh. 2019-05-03. A note on the consistency operator. https://arxiv.org/abs/1905.00998

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