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On existence of models for the logical system MPCL

We study whether a (Dedekind) cut has a model or not for the logical space of the logical system MPCL and for relations satisfying the MPC.1 law. The results depend on whether the quantity system is well-ordered and has the largest element or not. We apply the results to show a condition for a consistent subset to have a model. Another application is an alternative proof for the fact that the MPC.1 law is a characteristic law of the logical space of MPCL.