Automorphisms of concrete logics
Navara, Mirko ; Tkadlec, Josef
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 15-25 / Harvested from Czech Digital Mathematics Library
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The main result of this paper is Theorem 3.3: Every concrete logic (i.e., every set-representable orthomodular poset) can be enlarged to a concrete logic with a given automorphism group and with a given center. Since every sublogic of a concrete logic is concrete, too, and since not every state space of a (general) quantum logic is affinely homeomorphic to the state space of a concrete logic [8], our result seems in a sense the best possible. Further, we show that every group is an automorphism group of a concrete lattice logic and, on the other hand, we prove that this is not true for Boolean logics with a dense center. As a technical tool for pursuing the latter type of problems, we investigate the correspondence between homomorphisms of concrete logics and pointwise mappings of their domain. We prove that in a suitable topological representation of concrete logics, every automorphism is carried by a homeomorphism.

Publié le : 1991-01-01
Classification:  03G12,  06C15,  81C10,  81P10 
@article{116938,
     author = {Mirko Navara and Josef Tkadlec},
     title = {Automorphisms of concrete logics},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {15-25},
     zbl = {0742.06008},
     mrnumber = {1118285},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116938}
}

Navara, Mirko; Tkadlec, Josef. Automorphisms of concrete logics. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 15-25. http://gdmltest.u-ga.fr/item/116938/

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