Zur Einführung der transfiniten Zahlen.¶
von Neumann, J. (1923). Zur Einführung der transfiniten Zahlen. Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Cardinality
- 3. Cardinal number as equivalence class:
This sourceGives the now-standard definition of ordinals (each ordinal is the set of its predecessors), so that under choice every set is equinumerous with a unique least ordinal identified as its cardinal.
- 3. Cardinal number as equivalence class:
- Order
- Set theory uses the inclusion order
⊆(a partial order, complete lattice under union and intersection) and the cardinality order on cardinal numbers, building on von Neumann's (1923) ordinal constructionThis sourceDefines ordinals as the canonical well-ordered sets and establishes the rank-function machinery.
- Set theory uses the inclusion order
- Well-Foundedness (Well-Ordering)
- A well-founded structure consists of six interlocking components that together specify what it means for a relation to support no-infinite-descent reasoning, with the rank-function machinery descending from von Neumann (1923) and the modern axiomatic packaging codified in Jech (2003):
This sourceDefines ordinals as the canonical well-ordered sets and establishes the rank-function machinery.
- A well-founded structure consists of six interlocking components that together specify what it means for a relation to support no-infinite-descent reasoning, with the rank-function machinery descending from von Neumann (1923) and the modern axiomatic packaging codified in Jech (2003):
Verification¶
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