Rob EgrotMahidol University2020-01-272020-01-272019-06-01International Journal of Algebra and Computation. Vol.29, No.4 (2019), 699-711021819672-s2.0-85061753495https://repository.li.mahidol.ac.th/handle/20.500.14594/51220© 2019 World Scientific Publishing Company. We use model theoretic techniques and games to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of specified countable cardinalities correspond to intersections and unions, respectively.Mahidol UniversityMathematicsArticleSCOPUS10.1142/S021819671950022X