Statement:
UT(ℵ0,ℵ0,ℵ0,R): The union of a denumerable family of denumerable subsets of R is denumerable.
Howard_Rubin_Number: 6
Parameter(s): This form does not depend on parameters
This form's transferability is: Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Book references
Zermelo's Axiom of Choice, Moore, G.H., 1982
Note connections:
Note 3
Howard-Rubin Number | Statement | References |
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6 A | Every uncountable subset of R contains a condensation point. \ac{G.~Moore} \cite{1982} p 205 and 324, \ac{Sierpi\'nski} \cite{1918}. |
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6 B | Every uncountable subset of R has two condensation points. \ac{G.~Moore} \cite{1982} p 205 and 324, \ac{Sierpi\'nski} \cite{1918}. |
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6 C | If A⊆Rn and A⋂B is countable for every bounded B then A is countable. \ac{G.~Moore} \cite{1982} p 36, \ac{Keremedis/Howard/Rubin/Stanley/Tachtsis} \cite{1999}. |
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