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Heytingove algebre in interpretacije : delo diplomskega seminarja
ID Zavrtanik, Nace (Author), ID Cvetko-Vah, Karin (Mentor) More about this mentor... This link opens in a new window

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Abstract
V tem seminarskem delu definiramo nekaj osnovnih pojmov univerzalne algebre, kot so algebre, izrazi in raznoterosti. Definiramo pojem interpretacije. Uvedemo mreže, verige in Heytingove algebre ter dokažemo nekaj preprostejših dejstev o mrežah in operacijah na njih. Končno dokažemo, da so vse interpretacije omejenih distributivnih mrež v podrazred Heytingovih algeber, sestavljen iz verig, bodisi trivialne bodisi dualne.

Language:Slovenian
Keywords:algebre, izrazi, raznoterosti, mreže, Heytingove algebre, interpretacije
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2022
PID:20.500.12556/RUL-140908 This link opens in a new window
UDC:512
COBISS.SI-ID:122593795 This link opens in a new window
Publication date in RUL:21.09.2022
Views:639
Downloads:30
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Secondary language

Language:English
Title:Heyting Algebras and Interpretations
Abstract:
In this seminar paper, we introduce some basic concepts of universal algebra such as algebras, terms, and varieties. We define interpretations. Also, we define lattices, chains, and Heyting algebras, and procede to prove some simple facts about lattices and operations on lattices. Finally, we prove that all interpretations of bounded distributive lattices into the subclass of Heyting algebras which consists of chains, are either trivial or dual.

Keywords:algebras, terms, varieties, lattices, Heyting algebras, interpretations

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