Bernays and Set Theory

2009/01/04 by Akihiro Kanamori · 2 citations
Arts and Humanities · Mathematics · Psychology · #Calculus (dental) #Computer science #Economics #Epistemology #History and Theory of Mathematics #Mathematical economics #Mathematics #Order (exchange) #Philosophy #Philosophy and History of Science #Philosophy and Theoretical Science #Reflection (computer programming) #Set (abstract data type) #Set theory

paper · doi:10.2178/bsl/1231081769

openalex publication_date 2009/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Abstract We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.

Citations

• Über Grenzzahlen und Mengenbereiche
• Sur la notion de l'ordre dans la Théorie des Ensembles
• Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre.
• Untersuchungen �ber die Grundlagen der Mengenlehre. I
• Zur Hilbertschen Beweistheorie
• Some impredicative definitions in the axiomatic set theory
• Die Axiomatisierung der Mengenlehre
• A system of axiomatic set theory - Part VII
• Beweis, da� jede Menge wohlgeordnet werden kann
• A system of axiomatic set theory—Part II
• A system of axiomatic set theory—Part I
• Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
• Consistency-Proof for the Generalized Continuum-Hypothesis
• Axiom schemata of strong infinity in axiomatic set theory
• Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre
• On Von Neumann's Axiom System for Set Theory

Cited by

• Reflection principle [wikipedia]
• Von Neumann–Bernays–Gödel set theory [wikipedia]

Related

• Classical Set Theory: Theory of Sets and Classes
• Set theory and von Neumann algebras
• Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of Sets
• Modern Set
• Rethinking set theory