Livros e artigos selecionados

N. C. A. da Costa and F. A. Dória, ``Undecidability and incompleteness in classical mechanics, Int. J. Theor. Physics vol. 30, pp. 10411073 (1991) Proves that chaos theory is undecidable and, if axiomatized within set theory, incomplete in the sense of Gödel.

N. C. A. da Costa and F. A. Dória, ``An undecidable Hopf bifurcation with an undecidable fixed point, Int. J. Theor. Physics vol. 33, pp. 18851903 (1994). Settles a question raised by V. I. Arnold in the list of problems drawn up at the 1974 American Mathematical Society Symposium on the Hilbert Problems: is the stability problem for stationary points algorithmically decidable?

I. Stewart, ``Deciding the undecidable, Nature vol. 352, pp. 664665 (1991).

I. Stewart, From Here to Infinity, Oxford (1996). Comments on the undecidability proof for chaos theory.

J. Barrow, Impossibility  The Limits of Science and the Science of Limits, Oxford (1998). Describes the solution of Arnold's stability problem.

S. Smale, ``Problem 14: Lorenz attractor, in V. I. Arnold et al., Mathematics, Frontiers and Perspectives, pp. 285286, AMS and IMU (2000). Summarizes the obstruction to decidability in chaos theory described by da Costa and Dória.

F. A. Dória and J. F. Costa, ``Special issue on hypercomputation, Applied Mathematics and Computation vol. 178 (2006).

N. C. A. da Costa and F. A. Dória, ``Consequences of an exotic formulation for P = NP, Applied Mathematics and Computation vol. 145, pp. 655665 (2003) and vol. 172, pp. 13641367 (2006). The criticisms to the da CostaDória approach appear in the references in those papers.

N. C. A. da Costa, F. A. Dória and E. Bir, ``On the metamathematics of the P vs. NP question, to be published in Applied Mathematics and Computation (2007). Reviews the evidence for a conjectured consistency of P = NP with some strong axiomatic theory.

A. Syropoulos, Hypercomputation: Computing Beyond the ChurchTuring Barrier, Springer (2008). Describes the contribution to hypercomputation theories by da Costa and Dória, and sketches their contribution to the P = NP problem.