A Lindström-style theorem for finitary propositional weak entailment languages with absurdity
Guillermo Badía · Logic Journal of IGPL · 2016
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.