Sets in Relation Algebra - Part I,
por Hugo Nobrega, bolsista PIBIC-UFF.
In these talks we shall put the arithmetics of RA to use in developing
a notion of 'set' in the Algebra, which will come in handy in future applications.
For example, such sets are of utmost importance when one is interested in adding 'points' to RA,
which in turn are directly related to some important Completeness results,
as seen in Schmidt and Ströhlein's article
'Relation algebras: concept of points and representability'.
On the arithmetics of relation algebras,
por Petrucio Viana, IM-UFF.
The arithmetics of an algebraic system is the part of its theory
whose results are obtained without the use of set theoretical aparatus
(substructures, homomorphisms, products, etc.).
Relation algebras (RAs) were proposed by A. Tarski as an algebraic
system to formalize the calculus of relations of A. De Morgan,
S.C. Peirce, and E. Schroeder. RAs have a very intricate arithmetics.
As a matter of fact, all mathematics can be developed in this framework.
In this talk we will review some of the more basic results
and techniques of the relational algebraic arithmetics,
hoping to give a glimpse of the beauty underneath this theory.
Sheaves for non-categorists - Part 3,
por Eduardo Oc