Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre.¶
Fraenkel, A. A. (1922). Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre. Mathematische Annalen, 230-237.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Infinity
- the Zermelo-Fraenkel-Choice (ZFC) framework including Fraenkel's (1922) completion
This sourceIntroduces the axiom of replacement, completing (with Zermelo 1908) the ZF system.
- the Zermelo-Fraenkel-Choice (ZFC) framework including Fraenkel's (1922) completion
- Set and Membership
- Set and membership is the foundational vocabulary of modern mathematics, formalized in Zermelo-Fraenkel set theory with Choice (ZFC)
This sourceIntroduces the axiom of replacement, completing (with Zermelo 1908) the ZF system.
- Set and membership is the foundational vocabulary of modern mathematics, formalized in Zermelo-Fraenkel set theory with Choice (ZFC)
- Well-Foundedness (Well-Ordering)
- … up to order-isomorphism; two well-orderings of the same cardinality can have wildly different order types (ω, ω + ω, ω · ω, ω^ω, ε₀ all have cardinality ℵ₀ but differ in order type), a distinction Cantor (1883) drew already in the Grundlagen between cardinality and the finer ordinal-classification of well-orderings.
This sourceIntroduces the axiom of replacement, completing (with Zermelo 1908) the ZF system.
- … up to order-isomorphism; two well-orderings of the same cardinality can have wildly different order types (ω, ω + ω, ω · ω, ω^ω, ε₀ all have cardinality ℵ₀ but differ in order type), a distinction Cantor (1883) drew already in the Grundlagen between cardinality and the finer ordinal-classification of well-orderings.
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