caa a22 4500 445813954 CHVBK 20180317145220.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11083-010-9166-0 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9166-0 Generalized Priestley Quasi-Orders [Elektronische Daten] [Guram Bezhanishvili, Ramon Jansana] We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasi-orders (Adams, Algebra Univers 3:216-228, 1973; Cignoli et al., Order 8(3):299-315, 1991; Schmid, Order 19(1):11-34, 2002). We also introduce Vietoris families and prove that homomorphic images of bounded distributive meet-semilattices are dually characterized by Vietoris families. We show that this generalizes the well-known characterization (Priestley, Proc Lond Math Soc 24(3):507-530, 1972) of homomorphic images of a bounded distributive lattice by means of closed subsets of its Priestley space. We also show how to modify the notions of generalized Priestley quasi-order and Vietoris family to obtain the dual characterizations of subalgebras and homomorphic images of bounded implicative semilattices, which generalize the well-known dual characterizations of subalgebras and homomorphic images of Heyting algebras (Esakia, Sov Math Dokl 15:147-151, 1974). Springer Science+Business Media B.V., 2010 Distributive semilattices nationallicence Implicative semilattices nationallicence Heyting algebras nationallicence Duality theory nationallicence Bezhanishvili Guram Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut Jansana Ramon Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001, Barcelona, Spain aut Order Springer Netherlands 28/2(2011-07-01), 201-220 0167-8094 28:2<201 2011 28 11083 https://doi.org/10.1007/s11083-010-9166-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9166-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bezhanishvili Guram Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut NATIONALLICENCE 700 1- Jansana Ramon Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001, Barcelona, Spain aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/2(2011-07-01), 201-220 0167-8094 28:2<201 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer