FREGE MEETS ZERMELO: A PERSPECTIVE ON INEFFABILITY AND REFLECTION

DOI10.1017/S1755020308080192zbMath1217.03034OpenAlexW2116467396MaRDI QIDQ3580672

Gabriel Uzquiano, Stewart Shapiro

Publication date: 13 August 2010

Published in: The Review of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1755020308080192

zbMATH Keywords

foundations of mathematicsphilosophy of mathematicsreflection principlesaxiomatic set theory

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Philosophical and critical aspects of logic and foundations (03A05) Consistency and independence results (03E35) Axiomatics of classical set theory and its fragments (03E30)

Cites Work

• Frege's other program
• Well- and non-well-founded Fregean extensions
• Principles of reflection and second-order logic
• Abstraction and set theory
• Axiom schemata of strong infinity in axiomatic set theory
• Foundations of set theory. With the collaboration of Dirk van Dalen. 2nd revised ed
• Principles of reflection in axiomatic set theory
• Burgess on Plural Logic and Set Theory
• Prolegomenon To Any Future Neo‐Logicist Set Theory: Abstraction And Indefinite Extensibility
• Zermelo: definiteness and the universe of definable sets
• Zermelo and the Skolem Paradox
• Mathematics and Bleak House
• On Von Neumann's Axiom System for Set Theory
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