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Results tagged with independence-results
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user 109573
This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.
5
votes
Accepted
A surjection from square onto power: Is limit Hartogs/Lindenbaum number necessary?
In the Feferman-Levy model $M$ for $\mathbb{R}$ being a countable union of countable sets, there is $X$ with $|\mathcal{P}(X)| =^* |X^2|$
and $\aleph(X)=\aleph^*(X)=\omega_1.$
In this model, we can ex …
- 4,316
13
votes
What are some reasonable-sounding statements that are independent of ZFC?
Is there a vector space with three non-isomorphic Hilbert space structures? A negative answer is equivalent to the conjunction CH + SCH.
Pf: An infinite-dimensional Hilbert space with Hilbert dimensio …