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We give a detailed and self-contained introduction to the theory of $\lambda$-toposes and prove the following: 1) A $\lambda $-separable $\lambda $-topos(one whose defining site has a certain smallness property) has enough $\lambda$-points. 2) Given a $\kappa $-site, its classifying $\lambda $-topos is ofpresheaf type (assuming $\kappa \vartriangleleft \lambda =\lambda ^{<\lambda}$).

Every theory is eventually of presheaf type