•  23
    Second-Order Characterizable Cardinals and Ordinals
    Studia Logica 84 (3): 425-449. 2006.
    The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several known results for the case of finite characterizability are extended to infinite characterizability, and investigations of the second-order theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about the relationship between ordinal characterizability and ordinal arithmetic. The broader significance of cardinal characterizability …Read more
  •  8
    The Fraenkel‐Carnap question for Dedekind algebras
    with George Weaver
    Mathematical Logic Quarterly 49 (1): 92-96. 2003.
    It is shown that the second-order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second-order theory is categorical. It follows that the second-order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second-order theory of a Dedekind algebra is qu…Read more