Browsing Mathematics by Author "Jovanović, Aleksandar"
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Jovanović, Aleksandar (Beograd)[more][less]
Abstract: The dissertation consists of five chapters. The Chapters 1 and 2 contain the known results from the model theory and the set theory which are used in the other chapters. A classification of the properties of filters is given in Chapter 3. Some connections between combinatoric properties are made and the theorems about existence are also given. Ultraproducts are studied in Chapter 4. The structure of ultraproducts is connected with the structure of ultrafilters and cardinality of ultraproducts. Moreover, some other problems are studied, as the 2- cardinality problem. In the case of a measurable cardinal the connection with continuum problem is presented and several theorems of the cardinality of ultraproducts are proved. The problems about the real measure are studied in Chapter 5. The forcing is presented and by using results from Chapter 3 and Chapter 4 several properties are proved. The notion of norm of measure is introduced and some possible relations between additivity and norm of a measure are studied. Real large measurable cardinals are introduced analogously as the other large cardinals. The inspiration for this introduction were Solovay’s results of equconsistency of the theory ZDF + ”there is a measurable cardinal” and the theory ZDF+”there is a real measurable cardinal”. The relative consistency of the real large measurable cardinals with respect to ZDF+”the corresponding large cardinal” is proved by a generalization of Solovay’s forcing. URI: http://hdl.handle.net/123456789/683 Files in this item: 1
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