The language of Stratified Sets is confluent and strongly normalising
Murdoch J. Gabbay · Logical Methods in Computer Science · 2018
We study the properties of the language of Stratified Sets (first-order logic with $\in$ and a stratification condition) as used in TST, TZT, and (with stratifiability instead of stratification) in Quine's NF. We find that the syntax forms a nominal algebra for substitution and that stratification and stratifiability imply confluence and strong normalisation under rewrites corresponding naturally to $\beta$-conversion. Comment: arXiv admin note: text overlap with arXiv:1406.4060