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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Diamond principles and GCH
 Fuková, Kateřina ; Šaroch, Jan (advisor) ; Chodounský, David (referee)
Diamond principles and the generalized continuum hypothesis are assertions related to infinite combinatorics. This thesis studies various connections between these assertions. From numerous formulations of diamond principles, it explicitly mentions exactly two of them: ♢S and ♢∗ S. Apart from an overview of the basic notions involved in this study, the thesis also contains a concise proof of Shelah's theorem published in the paper "Diamonds" in 2010. 1
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Testing the projectivity of modules
 Matoušek, Cyril ; Šaroch, Jan (advisor) ; Žemlička, Jan (referee)
In this thesis, we study the problem of the existence of test modules for the projectivity. A right R-module is said to be a test module if it holds for every right R-module M that M is projective whenever T ∈ M⊥ . We show that test modules exist over right perfect rings, although their existence is not provable in ZFC in case of non-right perfect rings. In order to prove this, we use Shelah's uni- formization principle, which is independent of the axioms of ZFC. Furthermore, we show that test modules exist over rings of finite global dimension assuming the weak diamond principle, which is also independent of ZFC. 1
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