Ortokomplementární diferenční svazy

Abstract

T ematem t eto diplomov e pr ace je studium bin arn ho oper atoru 4, kter y mode- luje standardn symetrickou diferenci mno zin. Tento oper ator je studov an jednak samostatn e (v kapitole II), jednak s dopl nuj c svazovou strukturou (kapitola III a n asleduj c ). Je zavedena t r da ODL a jsou prozkoum any n ekter e jej z akladn vlast- nosti. D ale je uk az ana t r da HOR, kter a je podt r dou t r dy ODL a m a uzk y vztah ke t r d e Booleov ych algeber. V posledn kapitole je pops ana konstrukce voln eho ortokomplement arn ho diferen cn ho svazu se dv ema gener atory.

The theme of this thesis is the investigation of a binary operator, 4, that models the standard symmetric di erence of sets. This operator is studied both separately (in Chapter II) and with the supplementary lattice structure (Chapter III and the rest). The class ODL is introduced and some of its basic properties are investigated. Then there is exhibited the class HOR. The class HOR is a subclass of ODL which is closely related to the class of Boolean algebras. In the last Chapter there is described the construction of free orthocomplemented di erence lattice with two generators. 3