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We give a uniform construction of free pseudospaces of dimension n extendingwork by Baudisch and Pillay. This yields examples of $\omega$-stable theorieswhich are n-ample, but not (n+1)-ample. The prime models of these theories arebuildings associated to certain right-angled Coxeter groups.

The free pseudospace is n-ample, but not (n+1)-ample