Francisco Antonio Doria

Born: 1945

place: Rio de Janeiro, Brazil

BS (1968-Chemical Engineering) Federal University at Rio

PH.D. (1977-Mathematical Physics) Brazilian Center for Physical Research; Privatdocent (1979)

Professor Emeritas of Communications at Federal University and Chairman of the Research Center on Mathematical Theories of Communications

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In the two years between is Bachelors degree (1968) and studying graduate mathematics,, Professor Doria trained as a securities analyst with a member of Rio's Stock Exchange.

Professor Doria was one of the founders of the School of Communications at Federal University

RESEARCH

The recent research interests of Francisco Antonio Doria concern the existence of fast-growing recursive computable functions such that it is undecidable (in theories a sstrong as ZF) whether they are total or not. Those results have consequences to complexity theory in computer science, especially for the P =?NP problem. Main acievement is that [P =NP] is consistent with ZF, given some strong side metamathematical conditions.

Doria's main achievements bear on mathematical physics, logic, and the philosphy of science, some of which in wide-audience, bestselling books of I. Stewart, J. Casti, J. Horgan and J. Barrow. A discussion of the da Costa-Doria results in Dynamical systems theory has appeared in Nature:

• 1981-1984. Discovery of necessary and sufficient conditions for the existence of guage field copies in a classical nonabelian guage field theory.
• 1991. Proof of the undecidability and incompleteness of chaos theory
• 1991. A counterexample to Penrose's 1989 conjecture on the nonexistence of incomputible phenomena at the level of classical physics, and solution to a Wolfrain conjecture.
• 1994. Prove of the decidability and incompleteness of the theory of finite noncooperative Nash games. The thoery enyails the undecidability and incompleteness of the Arrow-Debreu theory of comnpetitive markets in economics.

SELECTED PUBLICATIONS

1. da Costa, N. C. A.; Doria, F. A. On set theory as a foundation for computer science. Bull. Sect. Logic Univ. \Lód\'z 33 (2004), no. 1, 33--40.
2. da Costa, N. C. A.; Doria, F. A. Consequences of an exotic definition for $\rm P=NP$. Appl. Math. Comput. 145 (2003), no. 2-3, 655--665.
3. Festschrift in honor of Newton C. A. da Costa on the occasion of his seventieth birthday. Edited by Décio Krause, Steven French and Francisco Antonio Doria. Synthese 125 (2000), no. 1-2. Kluwer Academic Publishers, Dordrecht, 2000. pp. i--iv and 1--299.
4. Doria, Francisco Antonio Is there a simple, pedestrian arithmetic sentence which is independent of ZFC? Festschrift in honor of Newton C. A. da Costa on the occasion of his seventieth birthday. Synthese 125 (2000), no. 1-2, 69--76.
5. Tsuji, Marcelo; da Costa, Newton C. A.; Doria, Francisco A. The incompleteness of theories of games. J. Philos. Logic 27 (1998), no. 6, 553--568.
6. Sant'Anna, A. S.; da Costa, N. C. A.; Doria, F. A. The Atiyah-Singer index theorem and the gauge field copy problem. J. Phys. A 30 (1997), no. 15, 5511--5516.
7. da Costa, N. C. A.; Doria, F. A. Structures, Suppes predicates, and Boolean-valued models in physics. Philosophical logic and logical philosophy, 91--118, Synthese Lib., 257, Kluwer Acad. Publ., Dordrecht, 1996.
8. Doria, Francisco Antonio Leopoldo Nachbin: some personal recollections. Contemporary Brazilian research in logic. Part I. Logique et Anal. (N.S.) 39 (1996), no. 153-154, 31--33.
9. Contemporary Brazilian research in logic. Part I. Edited by Jean-Yves Béziau and Francisco Antonio Doria. Logique et Anal. (N.S.) 39 (1996), no. 153-154. Centre National Belge de Recherches de Logique, Gent-Mariakerke, 1996. pp. 1--204.
10. Doria, Francisco Antonio Some new incompleteness theorems and their import to the foundations of mathematics. Contemporary Brazilian research in logic. Part I. Logique et Anal. (N.S.) 39 (1996), no. 153-154, 165--182.
11. da Costa, N. C. A.; Doria, F. A. Gödel incompleteness, explicit expressions for complete arithmetic degrees and applications. Complexity 1 (1995), no. 3, 40--55.
12. da Costa, Newton C. A.; Doria, Francisco A. Undecidability, incompleteness and Arnol\cprime d problems. Studia Logica 55 (1995), no. 1, 23--32.
13. da Costa, Newton C. A.; Doria, Francisco A.; Tsuji, Marcelo The undecidability of formal definitions in the theory of finite groups. Bull. Sect. Logic Univ. \Lód\'z 24 (1995), no. 2, 56--63.
14. da Costa, Newton C. A.; Doria, Francisco A. On Ja\'skowski's discussive logics. Studia Logica 54 (1995), no. 1, 33--60.
15. da Costa, Newton C. A.; Doria, Francisco Antonio Gödel incompleteness in analysis, with an application to the forecasting problem in the social sciences. Philos. Natur. 31 (1994), no. 1, 1--24.
16. Da Costa, N. C. A.; Doria, F. A. Suppes predicates and the construction of unsolvable problems in the axiomatized sciences. Patrick Suppes: scientific philosopher, Vol. 2, 151--193, Synthese Lib., 234, Kluwer Acad. Publ., Dordrecht, 1994.
17. da Costa, N. C. A.; Doria, F. A. Undecidable Hopf bifurcation with undecidable fixed point. Internat. J. Theoret. Phys. 33 (1994), no. 9, 1885--1903.
18. da Costa, N. C. A.; Doria, F. A.; Furtado-do-Amaral, A. F.; de Barros, J. A. Two questions on the geometry of gauge fields. Found. Phys. 24 (1994), no. 5, 783--800.
19. da Costa, N. C. A.; Doria, F. A. Incomplete satisfiability problems. Bull. Sect. Logic Univ. \Lód\'z 22 (1993), no. 4, 150--157.
20. da Costa, N. C. A.; Doria, F. A. On Arnol\cprime d's Hilbert symposium problems. Computational logic and proof theory (Brno, 1993), 152--158, Lecture Notes in Comput. Sci., 713, Springer, Berlin, 1993.
21. da Costa, N. C. A.; Doria, F. A.; Furtado do Amaral, A. F. Dynamical system where proving chaos is equivalent to proving Fermat's conjecture. Internat. J. Theoret. Phys. 32 (1993), no. 11, 2187--2206.
22. da Costa, Newton C. A.; Doria, Francisco Antonio On the incompleteness of axiomatized models for the empirical sciences. Philosophica 50 (1992), no. 2, 73--100.
23. da Costa, Newton C. A.; Doria, F. Antonio Suppes predicates for classical physics. The space of mathematics (San Sebastiàn, 1990), 168--191, Found. Comm. Cogn., de Gruyter, Berlin, 1992.
24.  da Costa, N. C. A.; Doria, F. A. On the existence of very difficult satisfiability problems. Bull. Sect. Logic Univ. \Lód\'z 21 (1992), no. 4, 122--133.
25. da Costa, Newton C. A.; Doria, Francisco Antonio Mathematics is dramatically incomplete. Theory, history and foundations of the formal sciences (Spanish). Theoria (San Sebastián) (2) 7 (1992), no. 16-18, A, 411--422.
26. da Costa, N. C. A.; Doria, F. A. Continuous & discrete: a research program. Bol. Soc. Paran. Mat. (2) 12/13 (1991/92), no. 1-2, 123--127 (1993).
27. da Costa, N. C. A.; Doria, F. A.; Papavero, N. Meinong's theory of objects and Hilbert's $\epsilon$-symbol. Rep. Math. Logic No. 25 (1991), 119--132.
28. da Costa, N. C. A.; Doria, F. A. Classical physics and Penrose's thesis. Found. Phys. Lett. 4 (1991), no. 4, 363--373.
29. da Costa, N. C. A.; Doria, F. A. Undecidability and incompleteness in classical mechanics. Internat. J. Theoret. Phys. 30 (1991), no. 8, 1041--1073.
30. da Costa, N. C. A.; Doria, F. A.; de Barros, J. A. A Suppes predicate for general relativity and set-theoretically generic spacetimes. Internat. J. Theoret. Phys. 29 (1990), no. 9, 935--961.
31. Doria, F. A.; de Barros, J. A.; Ribeiro da Silva, M. Noncomputable functions, generic functions and random sequences. Bol. Soc. Paran. Mat. (2) 8 (1987), no. 2, 197--216.
32. Doria, Francisco Antonio Chaos and nonalgorithmic functions. Bol. Soc. Paran. Mat. (2) 7 (1986), no. 2, 119--126.
33. Doria, F. A.; Abrahão, S. M.; do Amaral, A. F. Furtado Dirac-like equations for gauge fields. Progr. Theoret. Phys. 75 (1986), no. 6, 1440--1446.
34. Doria, Francisco Antonio A bifurcation set associated to the copy phenomenon in the space of gauge fields. Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981), 69--84, North-Holland Math. Stud., 86, North-Holland, Amsterdam, 1984.
35. Doria, F. A.; Ribeiro da Silva, M.; Furtado do Amaral, A. F. A generalization of Einstein's $\lambda$-transformation and gravitational copies. Lett. Nuovo Cimento (2) 40 (1984), no. 16, 509--512.
36. do Amaral, A. F. Furtado; Doria, F. A.; Gleiser, M. Higgs fields as Bargmann-Wigner fields and classical symmetry breaking. J. Math. Phys. 24 (1983), no. 7, 1888--1890.
37. Nachbin, Leopoldo The development of mathematical physics and related functional analysis, and its role in a developing country. (Portuguese) With remarks by Paul Krée. Translated from the English by F. A. Doria. Bol. Soc. Paran. Mat. (2) 2 (1981), no. 1, 17--26.
38. Doria, Francisco Antonio On the existence of the Wu-Yang ambiguity. An. Acad. Brasil. Ciênc. 53 (1981), no. 4, 657--660.
39. Doria, Francisco Antonio Quasi-abelian and fully nonabelian gauge field copies: a classification. J. Math. Phys. 22 (1981), no. 12, 2943--2951.
40. Doria, Francisco Antonio The geometry of gauge field copies. Comm. Math. Phys. 79 (1981), no. 3, 435--456.
41. Nachbin, Leopoldo The development of mathematical physics and related functional analysis, and its role in a developing country. (Portuguese) With remarks by Paul Krée. Translated from the English by Francisco Antonio Dória. Ciênc. Cultura 31 (1979), no. 9, 1001--1004.
42. Doria, Francisco Antonio Every nontrivial cocycle has an extension with a distribution singularity. An. Acad. Brasil. Ciênc. 51 (1979), no. 2, 207--209.
43. Doria, Francisco Antonio Noncontinuous gauge potentials without magnetic monopoles. J. Math. Phys. 20 (1979), no. 7, 1464--1465.
44. Doria, Francisco Antonio; Abrah ao, Sergio Murilo Mesonic test fields and spacetime cohomology. J. Math. Phys. 19 (1978), no. 8, 1650--1653.
45. Doria, F. A. On Teitler's higher-spin field equations. Lett. Nuovo Cimento (2) 18 (1977), no. 2, 37--40.
46. Doria, F. A. A Weyl-like equation for the gravitational field. Lett. Nuovo Cimento (2) 14 (1975), no. 13, 480--482.
47. Doria, F. A. Clifford-algebra formulation of multispin field equations. Lett. Nuovo Cimento (2) 8 (1973), 994--996. 81.4

references: Dr. Doria and his vita.

Francisco Antonio Doria is very proud of his black African heritage, and we welcome this acknowledgement.

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