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Results tagged with large-cardinals
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user 109573
12
votes
1
answer
318
views
Which $L$-like principles are known to be relatively consistent with large cardinals?
For which of the standard large cardinal axioms $\varphi_{LC}$ and which $L$-like principles $\psi$ (e.g. GCH, $\mathrm{V}=\mathrm{HOD},$ the ground axiom, and various diamond and square principles) i …
- 4,316
9
votes
Accepted
Can a Vopenka cardinal be supercompact?
If $\kappa$ is almost huge with target $\lambda,$ then $V_{\lambda}$ thinks that $\kappa$ is a supercompact Vopenka cardinal.
I'll take for granted the standard facts about almost huge cardinals liste …
- 4,316
11
votes
Accepted
What can be the measure of a Vitali set?
Let $\mu$ be a total extension of Lebesgue measure. For $\lambda>0,$ we define another total extension of Lebesgue measure by $\mu_{\lambda}(X)=\frac{1}{\lambda}(\lambda X).$ We will show there is $\l …
- 4,316