Developing arithmetic in set theory without infinity: some historical remarks

DOI10.1080/01445348708837116zbMath0644.03001OpenAlexW2037834323WikidataQ58342949 ScholiaQ58342949MaRDI QIDQ3786464

Charles Parsons

Publication date: 1987

Published in: History and Philosophy of Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01445348708837116

zbMATH Keywords

Zermeloaxiom of infinityFregeGödelvon NeumannQuineDedekindBernaysGrellinghistorical development of arithmetic in set theory

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematical logic and foundations (03-03)

Related Items (7)

TWO-SORTED FREGE ARITHMETIC IS NOT CONSERVATIVE ⋮ Kripke, Quine and Steiner on Representing Natural Numbers in Set Theory ⋮ Zermelo and Set Theory ⋮ Zigzag and Fregean Arithmetic ⋮ Frege's other program ⋮ Zermelo and Set Theory ⋮ Amending Frege's \textit{Grundgesetze der Arithmetik}

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• EIGHTY YEARS OF FOUNDATIONAL STUDIES
• A basis for number theory in finite classes
• Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory
• The theory of classes A modification of von Neumann's system
• A system of axiomatic set theory—Part I
• A system of axiomatic set theory—Part II
• A system of axiomatic set theory - Part VII
• Consistency of the Continuum Hypothesis. (AM-3)
• The axiom of choice

This page was built for publication: Developing arithmetic in set theory without infinity: some historical remarks