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Results tagged with big-list
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user 109573
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
22
votes
What notable theorems cannot be automatically proven without choice using Shoenfield absolut...
$\text{ZF}+ \text{AC}_{\omega}$ is not $\Sigma^1_4$-conservative over ZF and ZF + DC is not $\Sigma^1_4$-conservative over $\text{ZF}+ \text{AC}_{\omega}.$
An example of the former: the sentence $\ome …
- 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 …
- 4,316