Artin, E. [1927] Über die Zerlegung definiter Funktionen in Quadrate, Abhandlungen aus dem Mathematischen Seminar der Hansischen Unhersität, vol. 5, pp. 100–115.

Artin, E. and Schreier, O. [1926] Algebraische Konstruktion reeller Körper, Abhandlungen aus dent Mathematischen Seminar der Hansischen Unhersität, vol. 5, pp. 83–99.

Ax, J. [1968] The elementary theory of finite fields, Annals of Mathematics, ser. 2, vol. 88, pp. 239–271.

Ax, J. and Kochen, S. [1965a] Diophantine problems over local fields. I, American Journal of Mathematics, vol. 87, pp. 605–630.

Ax, J. and Kochen, S. [1965b] Diophantine problems over local fields. II: A complete set of axioms for p-adic number theory, American Journal of Mathematics, vol. 87, pp. 631–648.

Ax, J. and Kochen, S. [1966] Diophantine problems over local fields. **III**: *Decidable fields*, Annals of Mathematics, ser. 2, vol. 83, pp. 437–456.

Becker, E. [1986] On the real spectrum of a ring and its application to semialgebraic geometry, Bulletin (New Series) of the American Mathematical Society, vol. 5, pp. 19–60.

Blum, L. [1977] Differentially closed fields: a model-theoretic tour, Contributions to algebra (collection of papers dedicated to Ellis Kolchin), Academic Press, New York, pp. 37–61.

Brumfiel, G. W. [1979] Partially ordered rings and semi-algebraic geometry, London Mathematical Society Lecture Note Series, vol. 37, Cambridge University Press, Cambridge.

Chang, C. C. and Keisler, H. J. [1973] Model theory, North-Holland, Amsterdam.

Cherlin, G. and Dickmann, M. A. [1983] Real closed rings. II: Model theory, Annals of Pure and Applied Logic, vol. 25, pp. 213–231.

Shang-Ching, Chou [1984] Proving elementary geometry theorems using Wu's algorithm, Automated theorem proving: After 25 years, Contemporary Mathematics, vol. 29, American Mathematical Society, Providence, Rhode Island, pp. 243–286.

Cohen, P. J. [1969] Decision procedures for real and p-adic fields, Communications in Pure and Applied Mathematics, vol. 22, pp. 131–151.

Collins, G. E. [1975] Quantifier elimination for real closed fields by cylindrical algebraic decomposition, Automata theory and formal languages, second GI conference, Kaiserslautern, 1975, Lecture Notes in Computer Science, vol. 33, Springer-Verlag, Berlin, pp. 134–183.

Collins, G. E. [1982] Quantifier elimination for real closed fields: a guide to the literature, Computer algebra. Symbolic and algebraic computation, Computing Supplementum, vol. 4, Springer-Verlag, Vienna, pp. 79–81.

Coste, M. [1982] Ensembles semi-algébriques, Géométric algébrique réelle et formes quadratiques (Rennes, 1981), Lecture Notes in Mathematics, vol. 959, Springer-Verlag, Berlin, pp. 109–138.

Coste, M. and Coste-Roy, M. F. [1982] La topologie du spectre réel, Ordered fields and real algebraic geometry, Contemporary Mathematics, vol. 8, American Mathematical Society, Providence, Rhode Island, pp. 27–59.

Dahn, B. [1984] The limit behaviour of exponential terms, Fundamenta Mathematicae, vol. 124, pp. 169–186.

Delfs, H. and Knebusch, M. [1981] Semialgebraic topology over a real closed field. II: Basic theory of semialgebraic spaces, Mathematische Zeitschrift, vol. 178, pp. 175–213.

Delzell, C. N. [1984] A continuous, constructive solution to Hubert's 17th problem, Inventiones Mathematicae, vol. 76, pp. 365–384.

Denef, J. [1984] The rationality of the Poincaré series associated to the p-adic points on a variety, Inventiones Mathematicae, vol. 77, pp. 1–23.

Denef, J. and Van Den Dries, L. [1988] Real and p-adic subanalytic sets, Annals of Mathematics (to appear).

Dickmann, M. A. [1985] Applications of model theory to real algebraic geometry. A survey, Methods in mathematical logic (proceedings of the sixth Latin American symposium on mathematical logic, Caracas, 1983), Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, Berlin, pp. 76–150.

Van Den Dries, L. [1978] Model theory of fields, Thesis, University of Utrecht, Utrecht.

Van Den Dries, L. [1984] Algebraic theories with definable Skolem functions, this Journal, vol. 49, pp. 625–629.

Van Den Dries, L. [1986] A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bulletin (New Series) of the American Mathematical Society, vol. 15, pp. 189–193.

Eršov, Yu. L. [1965] On the elementary theory of maximal normed fields, Algebra i Logika, vol. 4, no. 3, pp. 31–70. (Russian)

Eršov, Yu. L. [1966] On the elementary theory of maximal normed fields. II, Algebra i Logika, vol. 5, no. 1, pp. 5–40. (Russian)

Eršov, Yu. L. [1967] On the elementary theory of maximal normed fields. III, Algebra i Logika, vol. 6, no. 3, pp. 31–38. (Russian)

Fried, M. and Jarden, M. [1986] Field arithmetic, Springer-Verlag, Berlin.

Gabrièlov, A. [1968] Projections of semi-analytic sets, Functional Analysis audits Applications, vol. 2, pp. 282–291.

Gorin, E. A. [1961] Asymptotic properties of polynomials and algebraic functions of several variables, Russian Mathematical Surveys, vol. 16, no. 1, pp. 93–119.

Grothendieck, A. [1964] Éléments de Géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. I, Institut des Hautes Études Scientifiques, Publications Mathématiques, vol. 20.

Grunewald, F. and Segal, D. [1980] Some general algorithms. I, II, Annals of Mathematics, ser. 2, vol. 112, pp. 531–583, 585–617.

Hardt, R. [1980] Semi-algebraic local triviality in semi-algebraic mappings, American Journal of Mathematics, vol. 102, pp. 291–302.

Henkin, L. [1960] Sums of squares, Summaries of talks presented at the summer institute for symbolic logic, Cornell University, 1957, 2nd ed., Institute for Defense Analyses, Princeton, New Jersey, pp. 284–291.

Hilbert, D. [1899] Grundlagen der Geometrie, Teubner, Leipzig.

Hironaka, H. [1973a] Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, pp. 453–493.

Hironaka, H. [1973b] Introduction to real-analytic sets and real-analytic maps, Lecture notes, Istituto Matematico “L. Tonelli”, Pisa.

Hörmander, L. [1955] On the theory of general partial differential operators, Acta Mathematica, vol. 94, pp. 161–248.

Hörmander, L. [1983] The analysis of linear partial differential operators. II, Springer-Verlag, Berlin.

Hovanskiĭ, A. G. [1980] On a class of systems of transcendental equations, Soviet Mathematics Doklady, vol. 22, pp. 762–765.

Hovanskiĭ, A. G. [1985] Fewnomials and Pfaff manifolds, Proceedings of the international congress of mathematicians (Warsaw, 1983), vol. 1, PWN, Warsaw, and North-Holland, Amsterdam, pp. 549–564.

Kreisel, G. [1960] Sums of squares, Summaries of talks presented at the summer institute for symbolic logic, Cornell University, 1957, 2nd ed., Institute for Defense Analyses, Princeton, New Jersey, pp. 313–320.

Lam, T. Y. [1984] An introduction to real algebra, Rocky Mountain Journal of Mathematics, vol. 14, pp. 767–814.

Łojasiewicz, S. [1964] Triangulations of semi-analytic sets, Annali delta Scuola Normale Superiore di Pisa, ser. 3, vol. 18, pp. 449–474.

Łojasiewicz, S. [1965] Ensembles semi-analytiques, Lecture notes, École Polytechnique, Paris.

Macintyre, A. [1976] On definable subsets of p-adic fields, this Journal, vol. 41, pp. 605–610.

Macintyre, A. [1986] Twenty years of p-adic model theory, Logic Colloquium '84, North-Holland, Amsterdam, pp. 121–153.

Macintyre, A., McKenna, K. and van den Dries, L. [1983] Elimination of quantifiers in algebraic structures, Advances in Mathematics, vol. 47, pp. 74–87.

Poizat, B. [1983] Une théorie de Galois imaginaire, this Journal, vol. 48, pp. 1151–1170.

Prestel, A. and Roquette, P. [1984] Formally p-adic fields, Lecture Notes in Mathematics, vol. 1050, Springer-Verlag, Berlin.

Robinson, A. [1955] On ordered fields and definite functions, Mathematische Annalen, vol. 130, pp. 257–271.

Robinson, A. [1956a] Complete theories, North-Holland, Amsterdam.

Robinson, A. [1956b] Further remarks on ordered fields and definite functions, Mathematische Annalen, vol. 130, pp. 405–409.

Robinson, A. [1957] Some problems of definability in the lower predicate calculus, Fundamenta Mathematicae, vol. 44, pp. 309–329.

Robinson, A. [1958] Relative model-completeness and the elimination of quantifiers, Dialectica, vol. 12, pp. 394–407.

Robinson, A. [1959a] On the concept of a differentially closed field, Bulletin of the Research Council of Israel, Section F: Mathematics and Physics, vol. 8, pp. 113–128.

Robinson, A. [1959b] Solution of a problem of Tarski, Fundamenta Mathematicae, vol. 47, pp. 179–204.

Robinson, A. and Zakon, E. [1960] Elementary properties of ordered Abelian groups, Transactions of the American Mathematical Society, vol. 96, pp. 222–236.

Robinson, J. [1949] Definability and decision problems in arithmetic, this Journal, vol. 14, pp. 98–114.

Sacks, G. E. [1972] Saturated model theory, Benjamin, Reading, Massachusetts.

Seidenberg, A. [1954] A new decision method for elementary algebra, Annals of Mathematics, ser. 2, vol. 60, pp. 365–374.

Seidenberg, A. [1956] An elimination theory for differential algebra, University of California Publications in Mathematics, New Series, vol. 3, pp. 31–66.

Shelah, S. [1973] Differentially closed fields, Israel Journal of Mathematics, vol. 16, pp. 314–328.

Shoenfield, J. L. [1971] A theorem on quantifier elimination, Symposia Mathematica, vol. 5 (INDAM, Rome, 1969/1970), Academic Press, London, pp. 173–176.

Shoenfield, J. L. [1977] Quantifier elimination in fields, Non-classical logics, model theory and computability (proceedings of the third Latin American symposium on mathematical logic, Campinas, 1976), North-Holland, Amsterdam, pp. 243–252.

Thom, R. [1962] La stabilité topologique des applications polynomials, L’Enseignement Mathématique, ser. 2, vol. 8, pp. 24–33.

Vaught, R. L. [1986] Tarski's work in model theory, this Journal, vol. 51, pp. 869–882.

van der Waerden, B. L. [1937] Moderne Algebra. Vol. I, 2nd ed., Springer-Verlag, Berlin.

Wang, Hao [1984] Computer theorem proving and artificial intelligence, Automated theorem proving: after 25 years, Contemporary Mathematics, vol. 29, American Mathematical Society, Providence, Rhode Island, pp. 49–70.

Wen-Tsün, Wu [1984] On the decision problem and the mechanization of theorem proving in elementary geometry, Automated theorem proving: after 25 years, Contemporary Mathematics, vol. 29, American Mathematical Society, Providence, Rhode Island, pp. 213–234.

Ziegler, M. [1982] Einige unentscheidbare Körpertheorien, L’Enseignement Mathématique, ser. 2, vol. 28, pp. 269–280; reprint, **Logic and algorithmic (Zurich, 1980)**, Monographies de L’Enseignement Mathématique, vol. 30, Université de Genève, Geneva, pp. 381–392.