Hypothesis: HR 43:
\(DC(\omega)\) (DC), Principle of Dependent Choices: If \(S\) is a relation on a non-empty set \(A\) and \((\forall x\in A) (\exists y\in A)(x S y)\) then there is a sequence \(a(0), a(1), a(2), \ldots\) of elements of \(A\) such that \((\forall n\in\omega)(a(n)\mathrel S a(n+1))\). See Tarski [1948], p 96, Levy [1964], p. 136.
Conclusion: HR 417:
On every non-trivial Banach space there is a non-trivial linear functional (bounded or unbounded).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|
Code: 3
Comments: