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The Multiplicity of Being: The Ontology of Alain Badiou
Pivoda, Tomáš ; Petříček, Miroslav (advisor) ; Kouba, Petr (referee) ; Pechar, Jiří (referee)
Tomáš Pivoda, The Multiplicity of Being: The Ontology of Alain Badiou PhD thesis Abstract The thesis introduces for the first time in the Czech philosophical context the ontology of the French philosopher Alain Badiou, as he set it out in his fundamental work Being and Event (L'être et l'événement, 1988). It first presents the starting point of Badiou's philosophy as well as the reasons of his identification of ontology with the set theory, and it points out Badiou's importance for contemporary philosophy, especially for the so called speculative realism around Quentin Meillassoux. The main axis of the exposition is then built around Badiou's four fundamental "Ideas": the multiplicity, the event, the truths and the subject, in connection with which it is shown how Badiou constructs his conceptual apparatus out of individual axioms of the set theory, whereby he follows the basic formal definition of multiplicity based on the operator . In connection with∈ the first Idea of multiplicity, the thesis exposes - with references to Martin Heidegger and Plato - Badiou's conceptual transposition of the couple one/multiple on the couple existence/being and defines the fundamental concepts of his ontology - the situation, the presentation, the representation and the void, with the help of which Badiou interprets...
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Modelling of exoplanetary atmospheric circulation
Novák, Jiří ; Brechler, Josef (advisor) ; Halenka, Tomáš (referee)
In this thesis we study the properties of exoplanetary atmospheres. The first part describes methods for searching exoplanets, statistics of discovered exoplanets and the sampling factors. The second part describes the properties of chosen planets and moons in the Solar system (Venus, Mars and Titan) and also possible properties of the exoplanetary atmospheres that are only briefly understood. The third part describes the atmospheric models which incorporate a full 3D model of the atmosphere, and a shallow- water model. We also show the results of exoplanetary atmospheric models published in the scientific journals. This part also describes the icosahedral geodetic grid that is advantageous for the global climatic models, and also discretisation on sphere and the application of the operators (gradient, divergence, vorticity) on geodetic grid. The last part is about creating program for global shallow water model in divergence-vorticity variables with forcing system with using icosahedral geodetic grid - we describe technical properties connected with model creating, parameters which the model uses during time integration, geographic system for results display and we show results for various kinds of extrasolar planets and planets in the Solar system. We used several numerical tests for testing model...
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Cohen forcing and its properties
Bydžovský, Jan ; Honzík, Radek (advisor) ; Verner, Jonathan (referee)
This bachelor thesis studies properties of Cohen Forcing and its relation to the unprovability of Continuum Hypothesis and Generalised Continuum Hypothesis. The thesis is divided into four parts. In the first part the technique of forcing based on partial orders is introduced. The second part introduces a notion of Cohen forcing, shows properties of cardinal arithmetic sufficient to preservation of cardinals by Cohen forcing and focuses mainly on generic sets added by concrete variations of Cohen Forcing. Finally some of the properties of Cohen reals are shown in this part. The third part reconstruct a proof of unprovability of Continuum Hypothesis and shows a use of Cohen Forcing in relation to the statements about the Generalised Continuum Hypothesis. The last part discusses briefly a non-minimality of generic filters on Cohen forcing and introduce a notion of Sacks forcing in order to show an existence of forcing notion whose generic filters are minimal. Keywords Cohen forcing, CH, GCH, Cohen reals.
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Forcing, deskriptivní teorie množin, analýza
Doucha, Michal ; Zapletal, Jindřich (advisor) ; Zelený, Miroslav (referee) ; Kubiš, Wieslaw (referee)
The dissertation thesis consists of two thematic parts. The first part, i.e. chapters 2, 3 and 4, contains results concerning the topic of a new book of the supervisor and coauthors V. Kanovei and M. Sabok "Canonical Ramsey Theory on Polish Spaces". In Chapter 2, there is proved a canonization of all equivalence relations Borel reducible to equivalences definable by analytic P-ideals for the Silver ideal. Moreover, it investigates and classifies sube- quivalences of the equivalence relation E0. In Chapter 3, there is proved a canonization of all equivalence relations Borel reducible to equivalences de- finable by Fσ P-ideals for the Laver ideal and in Chapter 4, we prove the canonization for all analytic equivalence relations for the ideal derived from the Carlson-Simpson (Dual Ramsey) theorem. The second part, consisting of Chapter 5, deals with the existence of universal and ultrahomogeneous Polish metric structures. For instance, we construct a universal Polish metric space which is moreover equipped with countably many closed relations or with a Lipschitz function to an arbitrarily chosen Polish metric space. This work can be considered as an extension of the result of P. Urysohn who constructed a universal and ultrahomogeneous Polish metric space.
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Logical background of forcing
Glivická, Jana ; Honzík, Radek (advisor) ; Chodounský, David (referee)
This thesis examines the method of forcing in set theory and focuses on aspects that are set aside in the usual presentations or applications of forcing. It is shown that forcing can be formalized in Peano arithmetic (PA) and that consis- tency results obtained by forcing are provable in PA. Two ways are presented of overcoming the assumption of the existence of a countable transitive model. The thesis also studies forcing as a method giving rise to interpretations between theories. A notion of bi-interpretability is defined and a method of forcing over a non-standard model of ZFC is developed in order to argue that ZFC and ZF are not bi-interpretable. 1
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The Multiplicity of Being: The Ontology of Alain Badiou
Pivoda, Tomáš ; Petříček, Miroslav (advisor) ; Kouba, Petr (referee) ; Pechar, Jiří (referee)
Tomáš Pivoda, The Multiplicity of Being: The Ontology of Alain Badiou PhD thesis Abstract The thesis introduces for the first time in the Czech philosophical context the ontology of the French philosopher Alain Badiou, as he set it out in his fundamental work Being and Event (L'être et l'événement, 1988). It first presents the starting point of Badiou's philosophy as well as the reasons of his identification of ontology with the set theory, and it points out Badiou's importance for contemporary philosophy, especially for the so called speculative realism around Quentin Meillassoux. The main axis of the exposition is then built around Badiou's four fundamental "Ideas": the multiplicity, the event, the truths and the subject, in connection with which it is shown how Badiou constructs his conceptual apparatus out of individual axioms of the set theory, whereby he follows the basic formal definition of multiplicity based on the operator . In connection with∈ the first Idea of multiplicity, the thesis exposes - with references to Martin Heidegger and Plato - Badiou's conceptual transposition of the couple one/multiple on the couple existence/being and defines the fundamental concepts of his ontology - the situation, the presentation, the representation and the void, with the help of which Badiou interprets...
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