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arXiv · 1207.4414

Model-theoretic characterization of intuitionistic propositional formulas

Grigory K. Olkhovikov
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Abstract

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is intuitionistically equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations between intuitionistic models.

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Grigory K. Olkhovikov. 2012-07-18. Model-theoretic characterization of intuitionistic propositional formulas. https://doi.org/10.1017/s1755020312000342

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