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Master's Dissertation
DOI
Document
Author
Full name
Lazaro Divino Assunção
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Bianconi, Ricardo (President)
Coniglio, Marcelo Esteban
Lopes, Vinicius Cifú
Title in Portuguese
Simplicidade e poder expressivo da geometria tarskiana
Keywords in Portuguese
Geometria
Geometria tarskiana
Abstract in Portuguese
Esta dissertação examinará dois temas no âmbito da geometria elementar. O primeiro tratará da expressividade da geometria de Alfred Tarski. Serão fornecidas as condições para que as fórmulas da geometria proposta por David Hilbert possam ser interpretadas na linguagem da geometria tarskiana. Por meio dessa interpretação, será apresentada uma prova de que os axiomas do sistema de Hilbert são teoremas no sistema da geometria elementar de Tarski. O segundo tema abordará o conceito de simplicidade em geometrias à la Tarski. Lançaremos mão de um sistema de axiomas devido a Victor Pambuccian, relativo à geometria hiperbólica; e, utilizando o critério sintático de simplicidade, mostraremos que esse sistema é o mais simples. Para finalizar, uma exposição dos pontos de vista de Jesse Alama e T. J. M. Makarios sobre simplificações na geometria elementar absoluta.
Title in English
Simplicity and expressive power of geometry Tarskian
Keywords in English
Geometry
Geometry Tarskian
Tarskian
Abstract in English
This dissertation will examine two themes in the realm of elementary geometry. The first theme will deal with the expressiveness of Alfred Tarskis geometry. The conditions for which formulae in the language of geometry proposed by David Hilbert can be interpreted in the one proposed by Alfred Tarski will be provided. By means of this interpretation, it will be presented a proof that the axioms of Hilberts system are theorems in the Tarskis elementary geometry system. The second theme will approach the concept of simplicity in Tarski like geometries. A system of axioms due to Victor Pambuccian which expresses the hyperbolic geometry is presented and, by using syntactical criterium of simplicity, it is shown that this system is the simplest possible. The dissertation ends with an exposition of points of view of Jesse Alama and T.J.M. Makarios about simplifications in elementary absolute geometry.
 
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Publishing Date
2019-11-04
 
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