In praise of replacement. (English) Zbl 1258.03001
Today, replacement is seen as a very basic set-theoretic principle. The author traces its history back to the times prior to its formal acceptance in the 1920s, discusses the way it became accepted as a basic axiom for set theory, describes its fundamental role within the ZFC axiomatic system, and looks finally at possible weakenings and their consequences for corresponding weakened set theories.
Reviewer: Siegfried J. Gottwald (Leipzig)
MSC:
| 03-03 | History of mathematical logic and foundations |
| 01A55 | History of mathematics in the 19th century |
| 01A60 | History of mathematics in the 20th century |
| 03E30 | Axiomatics of classical set theory and its fragments |
Keywords:
axiomatic set theory; axiom of replacement; history of mathematics; Zermelo; Fraenkel; SkolemReferences:
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