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Algebraic New Foundations
Journal of Symbolic Logic 84 (2):798-832 (2019)
Abstract
This paper consists in the formulation of a novel categorical set theory, MLCat, which is proved to be equiconsistent to New Foundations (NF), and which can be modulated to correspond to intuitionistic (denoted with an “I” on the left) or classical NF, with atoms (denoted with a “U” on the right) or not.Other Versions
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References found in this work
Frege's double correlation thesis and Quine's set theories NF and ML.Nino B. Cocchiarella - 1985 - Journal of Philosophical Logic 14 (1):1-39.
Automorphisms of models of set theory and extensions of NFU.Zachiri McKenzie - 2015 - Annals of Pure and Applied Logic 166 (5):601-638.
Relating first-order set theories, toposes and categories of classes.Steve Awodey, Carsten Butz, Alex Simpson & Thomas Streicher - 2014 - Annals of Pure and Applied Logic 165 (2):428-502.
Relational dual tableau decision procedures and their applications to modal and intuitionistic logics.Joanna Golińska-Pilarek, Taneli Huuskonen & Emilio Muñoz-Velasco - 2014 - Annals of Pure and Applied Logic 165 (2):409-427.
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