Does it make it more or less hostile than Stack Exchange?
and then when you click Legal notice, you see that all conditions and legal of Stack Exchange applies.
In addition:
> This letter is to confirm that, per our communications, that MathOverflow ("MathOverflow") agrees that the website, MathOverflow (located at www.mathoverflow.net, www.mathoverflow.com and www.mathoverflow. org (the "MathOverflow Domains"), the assets of which are owned and controlled by MathOverflow, will be upgraded to Stack Exchange, Inc.'s ("Stack Exchange") version 2.0 software model and, in conjunction with this upgrade, MathOverflow accepts Stack Exchange 2.0's Terms of Service (http://stackexchange.com/legal/tems-of-service, the "Terms"
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"completely independent" is perhaps exaggerated claim.
I think Math Overflow was the first overflow instance after SO, so it has a sort of a special status and its own domain. *.stackexchange.com came later to meet the growing demand for more instances.