Suslin's problem (Q2296408)

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the proposition, independent of ZFC, that a nonempty unbounded complete dense total order satisfying the countable chain condition is isomorphic to the reals

Language	Label	Description	Also known as
English	Suslin's problem	the proposition, independent of ZFC, that a nonempty unbounded complete dense total order satisfying the countable chain condition is isomorphic to the reals

Statements

mathematical concept

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defining formula

X\cong (\mathbb {R} ,\leq )\iff |X|>0\land \not \exists \max X\land \not \exists \min X\land (\forall x,y\in X\colon x<y\implies (x,y)\neq \varnothing )\land (\forall S\subset X\forall x\in X\colon (S<x\implies \exists \sup S\land x<S\implies \exists \inf S))\land (\forall I\forall a,b\colon I\to X\colon ((\forall i\in I\colon a_{i}<b_{i})\land \forall i\neq j\in I\colon (a_{i},b_{i})\cap (a_{j},b_{j})=\varnothing )\implies |I|<\aleph _{1})

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in defining formula

X

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totally ordered set

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\leq

symbol represents

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\mathbb {R}

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set of real numbers

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(a,b)

symbol represents

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

1 reference

Freebase Data Dumps

publication date

28 October 2013

Microsoft Academic ID

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Sitelinks

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