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UBC CS TR-91-17 Summary

On the CONSISTENCY and COMPLETENESS of an EXTENDED NaDSet, August 1991 Paul C. Gilmore, 54 pages

NaDSet in its extended form has been defined in several previous papers describing its applications. It is a {\underline N}atural {\underline D}eduction based {\underline Set} theory and logic. In this paper the logic is shown to enjoy a form of $\omega$-consistency from which simple consistency follows. The proof uses transfinite induction over the ordinals up to $\varepsilon_0$, in the style of Gentzen's consistency proof for arithmetic. A completeness proof in the style of Henkin is also given. Finally the cut rule of deduction is shown to be redundant.

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