Just to be pedantic – you’d call it “this wednesday” instead of “next wednesday”, even though it is technically the next Wednesday. English do be like that. I found this nice explanation:

Strictly speaking you would say "this coming Wednesday" for future events, and "this past Wednesday" for events in the past - but in most situations "future" and "past" tend to be omitted, as the timeline is implied by the context.
I went to the gym this Wednesday.
I will go to the gym this Wedneday.