numbers the definable numbers the real numbers superreal numbers hyperreal numbers the Puiseux series with real coefficients the surreal numbers Notes References Basu, Saugata, Richard Pollack, and Marie-Françoise Roy (2003) "Algorithms in real algebraic geometry" in Algorithms and computation in mathematics. Springer. (online version) Michael Ben-Or, Dexter Kozen, and John Reif, The complexity of elementary algebra and geometry, Journal of Computer and Systems Sciences 32 (1986), no. 2, pp. 251–264. Caviness, B F, and Jeremy R. Johnson, eds. (1998) Quantifier elimination and cylindrical algebraic decomposition. Springer. Chen Chung Chang and Howard Jerome Keisler (1989) Model Theory. North-Holland. Dales, H. G., and W. Hugh Woodin (1996) Super-Real Fields. Oxford Univ. Press. Macpherson, D., Marker, D. and Steinhorn, C., Weakly o-minimal structures and real closed fields, Trans. of the American Math. Soc., Vol. 352, No. 12, 1998. Mishra, Bhubaneswar (1997) "Computational Real Algebraic Geometry," in Handbook of Discrete and Computational Geometry. CRC Press. 2004 edition, p. 743. Alfred Tarski (1951) A Decision Method for Elementary Algebra and Geometry. Univ. of California Press. External links Real Algebraic and Analytic Geometry Preprint Server Model Theory preprint server Field (mathematics) Real algebraic geometry