The Hauptsatz for Stratified Comprehension - a Semantic Proof

(1994) Mathematical Logic Quarterly — Vol. 40, n° 4, p. 481-489 (1994)

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Abstract
We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i.e. Quine's NF minus extensionality.
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Crabbé, M. (1994). The Hauptsatz for Stratified Comprehension - a Semantic Proof. Mathematical Logic Quarterly, 40(4), 481-489. https://doi.org/10.1002/malq.19940400406 (Original work published 1994)