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The Divisibility Relation in Rings
Ketner, Michal ; Švejdar, Vítězslav (advisor) ; Honzík, Radek (referee)
This thesis aims to define a theory of divisibility for general integral domains. A hiear- chy of divisibility domains with properties to those of division on the integers is outlined. Chinese residue theorem is generalized by means of ideals in order to demonstrate wea- kening of generalization, that provides more effective tools. The thesis is prepared for all those interested in mathematics who want to get an insight into the theory of divisibility, so we build the theory from the beginning and compare it with division on integers. 1
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The Divisibility Relation in Rings
Ketner, Michal ; Švejdar, Vítězslav (advisor) ; Arazim, Pavel (referee)
This thesis aims to define a theory of divisibility for general integral domains. A hiear- chy of divisibility domains with properties to those of division on the integers is outlined. Chinese residue theorem is generalized by means of ideals in order to demonstrate wea- kening of generalization, that provides more effective tools. The thesis is prepared for all those interested in mathematics who want to get an insight into the theory of divisibility, so we build the theory from the beginning and compare it with division on integers. 1
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The constructive universe L
Ketner, Michal ; Honzík, Radek (advisor) ; Přenosil, Adam (referee)
The theme explores the universe of constructive set L as it was defined by Godel. The work compares two methods of construction L set: one through the formalization of satisfaction relationand the other one with several (finitely many) called rudimentary functions that generate L. The work continues with verification of the implications Con(ZF)→Con(ZFC + CH). The goal is to give a comprehensive view of the construction L and verification of 's relative consistency CH. Powered by TCPDF (www.tcpdf.org)
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The constructive universe L
Ketner, Michal ; Honzík, Radek (advisor) ; Přenosil, Adam (referee)
The theme explores the universe of constructive set L as it was defined by Godel. The work compares two methods of construction L set: one through the formalization of satisfaction relationand the other one with several (finitely many) called rudimentary functions that generate L. The work continues with verification of the implications Con(ZF)→Con(ZFC + CH). The goal is to give a comprehensive view of the construction L and verification of 's relative consistency CH. Powered by TCPDF (www.tcpdf.org)
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