Seminário remoto "Lógicos em Quarentena" 15/10/2020 (quinta-feira) 16:00h

[Bruno Lopes]

Numa iniciativa conjunta da Sociedade Brasileira de Lógica e do Grupo de Interesse em Lógica da Sociedade Brasileira de Computação, gostaríamos de convidar a todos a participarem do Seminário "Lógicos em Quarentena". Trata-se de um seminário remoto com apresentações informais por membros da comunidade e espaço para perguntas no fim. As apresentações usualmente são gravadas e disponibilizadas na página do evento http://lq.sbl.org.br (com a agenda completa).

Data: 15 de outubro de 2020 (quinta-feira)
Horário: 16:00h GMT-3
Apresentador: Hugo Luiz Mariano (IME/USP)
Título: An algebraic framework to a theory of sets based on the surreal numbers
Resumo: The surreal numbers constitute a linearly ordered (proper) class $No$

containing the class of all ordinal numbers ($On$), that satisfies many interesting properties. In an attempt to codify the universe of sets directly within the surreal number class, we have founded some clues that suggest that this class is not suitable for this purpose. Carefully formalizing the definition of the class of pre-(surreal) numbers (and some variants), which is an intermediate stage in the construction of the Conway surreal numbers, we obtain structures which have copies of $No$ as well the class the universe of all sets ($V$) as well as copies of the class of surreal numbers. Thus, in particular, we gave first steps toward a certain kind of "relative set theory", in this new setting.

The main aim of this work is to isolate and explore properties of these new constructions and present the notion of (partial) SUR algebra, an attempt to obtain an "algebraic theory for surreal numbers" along the lines of the Algebraic Set Theory of Joyal and Moerdijk: to establish (abstract and general) links between the class of all surreal numbers and a universe of "surreal sets" similar to the relations between the classes $On$ and $V$, of all ordinals and the class of all sets, that respects and expands the links between the linearly ordered class $On$ and $No$ of all ordinals and of all surreal numbers.

A apresentação ocorrerá pelo Google Meet através do link público https://meet.google.com/sqh-iepr-ges .

--

Bruno Lopes

Professor Adjunto

Instituto de Computação

Universidade Federal Fluminense

http://www.ic.uff.br/~bruno