(Q2296408)

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

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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

symbol represents

totally ordered set

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\leq

symbol represents

total order

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\mathbb {R}

symbol represents

set of real numbers

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(a,b)

symbol represents

open interval

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

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28 October 2013

Microsoft Academic ID

2775894269

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(Q2296408)

Suslin's problem

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