1. A finiteness theorem for open semialgebraic sets, with applications
to Hilbert's 17th problem,

in *Ordered Fields and Real Algebraic Geometry*,

D.W. Dubois and T. Recio, eds. Contemporary
Math., Vol. 8 (1982),

Amer. Math. Soc., pp. 79-97.
*Zbl.***
495** (1983), 14013. *MR***83h**:12033.

2. Case distinctions are necessary for representing polynomials as sums
of squares,

in
*
Proc. Herbrand Symp., Logic Coll. 1981,*

Stud. Logic Found. Math. 107,

J. Stern, ed. North Holland, 1982, pp. 87-103.
*Zbl.***
502** (1983), 03032. *MR***86i**:11015.

3. Continuous sums of squares of forms,

in
*L.E.J. Brouwer Centenary Symp.*,

Stud. Logic Found. Math. 110,

A.S. Troelstra and D. van Dalen, eds.

North Holland, 1982, pp. 65-75.
*Zbl.***
527** (1984), 10016. *MR***85g**:03086.

4. A continuous, constructive solution to Hilbert's 17th problem,
*Invent.
math.*** 76**(3)
(1984), 365-84.
*Zbl.*
547 (1985), 12017. *MR***86e**:12003.

Also reviewed by I. Stewart,

The power of positive thinking,
*Nature***
315** (13 June 1985), 539;

and by *Math. Magazine*
**59**(1) (Feb. 1986), 55.

5. Piecewise-rational retractions onto closed, convex semi-algebraic
sets with interior--synopsis,
*Rocky
Mountain J. Math.* **14**(4) (Fall 1984), 943-6.
*Zbl. ***571**
(1986), 14014. *MR***86f**:12009.

6. Analytic right-inverses for quadratic forms over number fields,
*Bull.
London Math. Soc.* **17**(5)
(1985), 449-52.
*Zbl.***
595** (1987), 10014. *MR***87b**:11029.

7. Note on quantifier prefixes over diophantine equations,
*Zeitschr. math. Logik Grundlagen Math.* (replaced by
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03004. *MR***88e**:03062.

8. Continuous Pythagoras numbers for rational quadratic forms,
*J. Number Theory***26**(3)
(1987), 257-73.
*Zbl.***626**
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*Computer & Info. Sys. Abst.* **36**(3), #88-04305C.

9. Correction to ``Note on quantifier prefixes over diophantine equations,''
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03003. *MR***89b**:03072.

10. On the Pierce-Birkhoff conjecture over ordered fields,
*Rocky
Mountain J. Math.* **19**(3)
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*Zbl.*
715, 14047. *MR***91b**:14073.

11. A new rational and continuous solution for the Hilbert's 17th problem,
*Extracta
Mathematicae* **7**(1)
(1992), 59-64

(with L.
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Lombardi).
*MR***93j**:12002.

12. A continuous and rational solution to Hilbert's 17th problem, and
several cases of the Positivstellensatz,

in Computational Algebraic Geometry, F. Eyssette, A. Galligo, eds.

Progress
in Math., Vol. 109, Birkhäuser (1993), 61-75

(with L.
Gonzalez-Vega and H.
Lombardi).
*MR***94f**:12001.

(A preprint of this was also published by

Departamento de Matematicas, Estadistica y Computacion, of the Universidad
de Cantabria (Spain),

Num. 9 (Julio 1992), 1-14.)

13. Continuous sums of squares of rational functions,

Seminaire de Structures Algebriques Ordonees 1991-1992,

Num. 42 (Fevrier 1993), F. Delon, M.A. Dickmann, D. Gondard, eds.,

Equipe de Logique Mathematique, Prepublications, Univ. Paris VII (CNRS),
1-6.

14. Continuous, piecewise-polynomial functions which solve Hilbert's
17th problem,
*J. reine angew.
Math.* **440**
(1993), 157--73.
*MR***94d**:12001.

15. Non-existence of analytically varying solutions to Hilbert's 17th
problem,

in *Recent Advances in Real Algebraic Geometry and Quadratic Forms,*
*Proc. RAGSQUAD Year, Berkeley, 1990-1991*,

W. Jacob, et al, eds. Contemp.
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*MR***95e**:12003.

16. A completely normal spectral space that is not a real spectrum,
*J. Algebra***169**(1)
(Oct. 1, 1994), 71-7 (with J.
Madden).
*MR***95g**:14061.

17. Lattice-ordered rings and semialgebraic geometry: I,

in *Real Analytic and Algebraic Geometry (Trento, 1992)*,

F. Broglia, et al, eds. , de Gruyter (1995), 103-29 (with J.
Madden).
*MR***96a**:14061.

18. Impossibility of C-infinity variation or formal power series variation

in solutions to Hilbert's 17th problem,
*J. Algebra* **275** (2004), 233-49.

**B. Long article:**

Kreisel's unwinding of Artin's proof,

in *Kreiseliana: About and Around Georg Kreisel*,

P. Odifreddi, ed., A K Peters, 1996, 113-246.
*CMP*
1 435 764, *MR***97m**:01097.

**C. Books:**

1. *Real algebraic geometry and ordered structures.*
*Papers from the special semester (RAGOS) and AMS Special Session*
*on Real Algebraic Geometry and Ordered Algebraic Structures*
*held at Louisiana State University, Baton Rouge, LA, January-May
and April 17-21, 1996*.

Edited by Charles N. Delzell and James J. Madden.

Contemp.
Math., **253**. AMS, Providence, RI, 2000. xxviii+287 pp. ISBN:
0-8218-0804-4.
*MR*2000m:14001.

2. *Positive
Polynomials: From Hilbert's 17th Problem to Real Algebraic Geometry*,

by Alexander
Prestel and Charles N. Delzell,

Springer
Monographs in Mathematics, 2001. 267 pp.

*MR *2002k:13044.

Click here for a list of Errata
and Updates for this book.

**D. Abstracts:**

(Under construction.)

Last updated September 18, 2005.