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If I restrict a variable x to x>0 via $Assumptions=x>0, is there a way I can get Mathematica to tell me that x>0? I would have guessed typing Attributes[x] would say something, but it gives {}.

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I don't yet have the reputation for commenting, but perhaps this suffices as an answer as well: why not just evaluate $Assumptions to get a list of active global assumptions about variables?

$Assumtions=x>0
$Assumptions
(*x>0*)
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    $\begingroup$ (+1) in case #Assumptions is a long list involving other variables, you can filter using Cases[_[___, x, ___]]@$Assumptions or Select[Not@*FreeQ[x]]@$Assumptions $\endgroup$
    – kglr
    Feb 18 at 5:19

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