Cutolo, Raffaella (2017) Berkeley Cardinals and the search for V. [Tesi di dottorato]

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Item Type: Tesi di dottorato
Lingua: English
Title: Berkeley Cardinals and the search for V
Creators:
CreatorsEmail
Cutolo, Raffaellaraffaella.cutolo@unina.it
Date: 7 April 2017
Number of Pages: 65
Institution: Università degli Studi di Napoli Federico II
Department: Matematica e Applicazioni "Renato Caccioppoli"
Dottorato: Scienze matematiche e informatiche
Ciclo di dottorato: 29
Coordinatore del Corso di dottorato:
nomeemail
de Giovanni, Francescofrancesco.degiovanni2@unina.it
Tutor:
nomeemail
Andretta, AlessandroUNSPECIFIED
Date: 7 April 2017
Number of Pages: 65
Uncontrolled Keywords: Berkeley Cardinals; strong axioms of infinity; universe of set theory
Settori scientifico-disciplinari del MIUR: Area 01 - Scienze matematiche e informatiche > MAT/01 - Logica matematica
Date Deposited: 20 Apr 2017 09:41
Last Modified: 14 Mar 2018 11:20
URI: http://www.fedoa.unina.it/id/eprint/11570
DOI: 10.6093/UNINA/FEDOA/11570

Abstract

This thesis is concerned with Berkeley Cardinals, very large cardinal axioms inconsistent with the Axiom of Choice. These notions have been recently introduced by J. Bagaria, P. Koellner and W. H. Woodin; our aim is to provide an introductory account of their features and of the motivations for investigating their consequences. As a noteworthy advance in the topic, we establish the independence from ZF of the cofinality of the least Berkeley cardinal, which is indeed the main point to focus on when dealing with the failure of Choice. We then explore the structural properties of the inner model L(V_\delta+1) under the assumption that delta is a singular limit of Berkeley cardinals each of which is a limit of extendible cardinals, lifting some of the theory of the axiom I_0 to the level of Berkeley cardinals. Finally, we discuss the role of Berkeley cardinals within the ultimate project of attaining a "definitive" description of the universe of set theory.

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