2009/07/01 by Laurence Kirby · 1 citation
Computer Science · Mathematics · #Adjunction #Algebra over a field #Basis (linear algebra) #Computability, Logic, AI Algorithms #Computer science #Discrete mathematics #Finitary #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Operator (biology) #Primitive recursive function #Programming language #Pure mathematics #Schema (genetic algorithms) #Set (abstract data type)
paper · pdf · doi:10.1215/00294527-2009-009
openalex publication_date 2009/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
I argue for the use of the adjunction operator (adding a single new element to an existing set) as a basis for building a finitary set theory. It allows a simplified axiomatization for the first-order theory of hereditarily finite sets based on an induction schema and a rigorous characterization of the primitive recursive set functions. The latter leads to a primitive recursive presentation of arithmetical operations on finite sets.