•  48
    Mildness and the Density of Rational Points on Certain Transcendental Curves
    with G. O. Jones and D. J. Miller
    Notre Dame Journal of Formal Logic 52 (1): 67-74. 2011.
    We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions
  •  24
    Approximating Cartesian Closed Categories in NF-Style Set Theories
    Journal of Philosophical Logic 47 (1): 143-160. 2018.
    I criticize, but uphold the conclusion of, an argument by McLarty to the effect that New Foundations style set theories don’t form a suitable foundation for category theory. McLarty’s argument is from the fact that Set and Cat are not Cartesian closed in NF-style set theories. I point out that these categories do still have a property approximating Cartesian closure, making McLarty’s argument not conclusive. After considering and attempting to address other problems with developing category theo…Read more
  •  29
    A Generalization of the Routley-Meyer Semantic Framework
    Journal of Philosophical Logic 44 (4): 411-427. 2015.
    We develop an axiomatic theory of “generalized Routley-Meyer logics.” These are first-order logics which are can be characterized by model theories in a certain generalization of Routley-Meyer semantics. We show that all GRM logics are subclassical, have recursively enumerable consequence relations, satisfy the compactness theorem, and satisfy the standard structural rules and conjunction and disjunction introduction/elimination rules. We also show that the GRM logics include classical logic, in…Read more