The course explores the notion of formal systems, from a completely abstract point of view. First, the intuitive concept of computability is introduced via examples, which will be used as evidence of the fundamental properties shared by all computing systems. The concept of Abstract Families of Algorithms (AFA) is introduced, as a group of algorithms with a certain computing power. The possibility of isomorphically transforming an AFA into another by means of algorithms in the families themselves is used to strongly support the Church-Turing thesis. Finally, an abstract version of Gödel's Incompleteness Theorem is presented.

References:
1. W.S. Brainerd and L.H. Landweber. Theory of Computation. Wiley, New York, 1974.
2. Roberto Lins de Carvalho e Claudia Maria Garcia Medeiros de Oliveira. Modelos de Computacao e Sistemas Formais. 11a Escola de Computacao, Rio de Janeiro, julho de 1998.
3. Raymond M. Smullyan. Theory of Formal Systems. Annals of Mathematics Studies. Princenton University Press, 1996.