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)

thesis: ; advisor: Leopold Nachbin

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

personal or universal URL:

email:

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 [

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**

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - da Costa, Newton C. A.; Doria, Francisco A. Undecidability,
incompleteness and Arnol\cprime d problems.
*Studia Logica***55**(1995), no. 1, 23--32. - 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. - da Costa, Newton C. A.; Doria, Francisco A. On Ja\'skowski's
discussive logics.
*Studia Logica***54**(1995), no. 1, 33--60. - 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. - 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. - 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. - 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. - da Costa, N. C. A.; Doria, F. A. Incomplete satisfiability
problems.
*Bull. Sect. Logic Univ. \Lód\'z***22**(1993), no. 4, 150--157. - 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. - 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. - 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. - 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. - 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. - 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. - 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). - 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. - da Costa, N. C. A.; Doria, F. A. Classical physics and Penrose's
thesis.
*Found. Phys. Lett.***4**(1991), no. 4, 363--373. - da Costa, N. C. A.; Doria, F. A. Undecidability and incompleteness
in classical mechanics.
*Internat. J. Theoret. Phys.***30**(1991), no. 8, 1041--1073. - 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. - 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. - Doria, Francisco Antonio Chaos and nonalgorithmic functions.
*Bol. Soc. Paran. Mat. (2)***7**(1986), no. 2, 119--126. - 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. - 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. - 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. - 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. - 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. - Doria, Francisco Antonio On the existence of the Wu-Yang
ambiguity.
*An. Acad. Brasil. Ciênc.***53**(1981), no. 4, 657--660. - Doria, Francisco Antonio Quasi-abelian and fully nonabelian
gauge field copies: a classification.
*J. Math. Phys.***22**(1981), no. 12, 2943--2951. - Doria, Francisco Antonio The geometry of gauge field copies.
*Comm. Math. Phys.***79**(1981), no. 3, 435--456. - 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. - Doria, Francisco Antonio Every nontrivial cocycle has an
extension with a distribution singularity.
*An. Acad. Brasil. Ciênc.***51**(1979), no. 2, 207--209. - Doria, Francisco Antonio Noncontinuous gauge potentials without
magnetic monopoles.
*J. Math. Phys.***20**(1979), no. 7, 1464--1465. - Doria, Francisco Antonio; Abrah ao, Sergio Murilo Mesonic
test fields and spacetime cohomology.
*J. Math. Phys.***19**(1978), no. 8, 1650--1653. - Doria, F. A. On Teitler's higher-spin field equations.
*Lett. Nuovo Cimento (2)***18**(1977), no. 2, 37--40. - Doria, F. A. A Weyl-like equation for the gravitational field.
*Lett. Nuovo Cimento (2)***14**(1975), no. 13, 480--482. - 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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