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TEORIA DEGLI INSIEMI
|TEORIA DEGLI INSIEMI /a||MAT/01||LEZIONI||42|
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KnowledgeThe student who successfully completes the course will have the ability to understand any modern treatise in set theory; will be able to demonstrate a solid knowledge of basic results in cardinal arithmetic; will be aware of the existing problems in axiomatic set theory and of the main current techniques to face these problems (inner models, forcing).
Assessment criteria of knowledge- During the oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression. The student is also presented some simple problems arising in the topics dealt with during the course
- Final oral exam
- Oral report
Delivery: face to face
- attending lectures
- preparation of oral/written report
- individual study
SyllabusAxiomatic set theory: review of the axiom systems ZFC and GB, as conservative extension; ZFA and ZF-, symmetric models without choice. Cardinal arithmetic: exponential and theorems of Buchowski; GCH and SCH. Transitive models of ZFC, transitive collapse and reflection principles. The class L of Goedel constructible sets. Consistency of AC and GCH. Boolean valued models and forcing: independence results through generic models.
BibliographyRecommended reading includes the following works; further bibliography will be indicated. T. Jech - Set theory. Academic Press
Ultimo aggiornamento 14/11/2016 17:27