Abstract
Following a result by De Rijke for modal logic, it is shown that the basic weak entailment model-theoretic language with absurdity is the maximal model-theoretic language having (i) the finite occurrence property, (ii) preservation under relevant directed bisimulations and (iii) the finite depth property. This can be seen as a generalized preservation theorem characterizing propositional weak entailment formulas among formulas of other model-theoretic languages.
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