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Lógica Matemática

An introduction to impredicative ordinal notation systems

David Fernandéz-Duque
Université Paul Sabatier, Toulouse

Abstract: In this course we will give an introduction to ordinal notation systems based on collapsing cardinals in the style of Buchholz. Although familiarity with proof-theoretic ordinals is assumed, the course will work gradually, beginning with a quick review of predicative notation systems and introducing some intermediate systems along the way. The course will be divided in two sessions.

Predicative ordinal notations (II)

João Enes
CMAFCIO, Universidade de Lisboa

Abstract: In this talk we will present the standard ordinal notation system for ordinals less than $\varepsilon_0$. We will introduce the Veblen hierarchy of functions based on the class of additively indecomposable ordinals. This will allow us to go beyond $\varepsilon_0$ and present a notation system for ordinals less than the Feferman-Schütte ordinal $\Gamma_0$.

Predicative ordinal notations (I)

João Enes
CMAF-CIO, Universidade de Lisboa

Abstract: In this talk we will present the standard ordinal notation system for ordinals less than $\varepsilon_0$. We will introduce the Veblen hierarchy of functions based on the class of additively indecomposable ordinals. This will allow us to go beyond $\varepsilon_0$ and present a notation system for ordinals less than the Feferman-Schütte ordinal $\Gamma_0$.

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