Order theory

Aronszajn line

In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality which contains no subset order-isomorphic to * with the usual ordering * the reverse of * an uncountable subset of the Real numbers with the usual ordering. Unlike Suslin lines, the existence of Aronszajn lines is provable using the standard axioms of set theory. A linear ordering is an Aronszajn line if and only if it is the lexicographical ordering of some Aronszajn tree. (Wikipedia).

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From playlist Logic and Foundations

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From playlist Logic and Foundations

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From playlist Student Competition: Computer Vision Training

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From playlist Multivariable Spaces and Functions

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Related pages

Uncountable set | Suslin's problem | Nachman Aronszajn | Aronszajn tree | Total order | Set theory | Real number | Order isomorphism