Axiomatic Set Theory à la Dijkstra and Scholten

The algebraic approach by E.W. Dijkstra and C.S. Scholten to formal logic is a proof calculus, where the notion of proof is a sequence of equivalences proved – mainly – by using substitution of ‘equals for equals’. This paper presents Set , a first-order logic axiomatization for set theory using the approach of Dijkstra and Scholten. What is novel about the approach presented in this paper is that symbolic manipulation of formulas is an effective tool for teaching an axiomatic set theory course to sophomore-year undergraduate students in mathematics. This paper contains many examples on how argumentative proofs can be easily expressed in Set and points out how the rigorous approach of Set can enrich the learning experience of students. The results presented in this paper are part of a larger effort to formally study and mechanize topics in mathematics and computer science with the algebraic approach of Dijkstra and Scholten.

• Autores: Acosta, Ernesto; Aldana, Bernarda; Bohórquez, Jaime; Rocha, Camilo
• Tipo de recurso: Part of book
• Fecha de publicación: 2017
• Institución: Escuela Colombiana de Ingeniería Julio Garavito
• Repositorio: Repositorio Institucional ECI
• Idioma: eng
• OAI Identifier: oai:repositorio.escuelaing.edu.co:001/1836
• Acceso en línea: https://repositorio.escuelaing.edu.co/handle/001/1836
• Palabra clave: Teoría axiomática de conjuntos; Lógica de Dijkstra-Scholten; Manipulación simbólica; SET; Axiomatic set theory; Dijkstra-Scholten logic; Derivation; Formal system; Zermelo-Fraenkel (ZF); Symbolic manipulation; Undergraduate-level course
• Rights: closedAccess
• License: © Springer Nature Switzerland AG 2018