Suslin's problem (Q2296408)

From Wikidata

Jump to navigation Jump to search

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

Sprache	Label	Description	Also known as
Englisch	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

0 references

0 references

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})

0 references

in defining formula

X

symbol represents

totally ordered set

0 references

\leq

symbol represents

0 references

\mathbb {R}

symbol represents

set of real numbers

0 references

(a,b)

symbol represents

0 references

maintained by WikiProject

WikiProject Mathematics

0 references

Identifiers

1 reference

Freebase Data Dumps

publication date

28 October 2013

Microsoft Academic ID

0 references

Sitelinks

Wikipedia(11 entries)

Wikibooks(0 entries)

Wikinews(0 entries)

Wikiquote(0 entries)

Wikisource(0 entries)

Wikiversity(0 entries)

Wikivoyage(0 entries)

Wiktionary(0 entries)

Multilingual sites(0 entries)

Retrieved from "https://www.wikidata.org/w/index.php?title=Q2296408&oldid=2241503504"