# Dependent choice as a termination principle

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## Abstract

We introduce a new formulation of the axiom of dependent choice, which can be viewed as an abstract termination principle that in particular generalises recursive path orderings, the latter being fundamental tools used to establish termination of rewrite systems. We consider several variants of our termination principle, and relate them to general termination theorems in the literature.

## Keywords

Dependent choice Arithmetic in all finite types Termination Path orderings Higher order reverse mathematics## Mathematics Subject Classification

03F03 03B15 03B70## Notes

### Acknowledgements

I am grateful to the anonymous referees for their many comments and corrections. I am also indebted to Georg Moser for suggesting the proof theoretic study of abstract path orderings, and to Sam Sanders for further comments on an earlier draft of this work.

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