Abstract
This chapter is devoted to model theory. Model theory is a general study of mathematical structures such as groups, rings, fields, and several other mathematical structures. Model theory is used to prove substantial results in conventional mathematics such as number theory, algebra, and algebraic geometry. Also, questions from logic pertaining to conventional mathematical structures throw up a good challenge to logic. This interplay between mathematics and logic has grown into very fascinating mathematics and is a very active area of research today. Chapter 2 should be considered as a part of model theory where, for example, embeddings, isomorphisms, homogeneous structures, and definability have been introduced and some important results are proved.
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References
Ax, J.: The elementary theory of finite fields. Ann. Math. 88, 103–115 (1968)
Bochnak, J., Coste, M., Roy, M-F.: Real Algebraic Geometry, vol. 36, A Series of Modern Surveys in Mathematics. Springer, New York (1998)
Chang, C.C., Keisler, H.J.: Model Theory, 3rd edn. North-Holland, London (1990)
Flath, D., Wagon, S.: How to pick out integers in the rationals: An application of number theory to logic. Am. Math. Mon. 98, 812–823 (1991)
Hinman, P.: Fundamentals of Mathematical Logic. A. K. Peters (2005)
Hofstadter, D.R.: Gödel, Escher, Bach: An Eternal Golden Braid. Vintage Books, New York (1989)
Hrushovski, E.: The Mordell–Lang conjecture for function fields. J. Am. Math. Soc. 9(3), 667–690 (1996)
Jech, T.: Set Theory, Springer Monographs in Mathematics, 3rd edn. Springer, New York (2002)
Kunen, K.: Set Theory: An Introduction to Independence Proofs. North-Holland, Amsterdam (1980)
Lang, S.: Algebra, 3rd edn. Addison-Wesley (1999)
Marker, D.: Model Theory: An Introduction, GTM 217. Springer, New York (2002)
Rogers, H.J.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)
Penrose, R.: The Emperor’s New Mind. Oxford University Press, Oxford (1990)
Pila, J.: O-minimality and André-Oort conjecture for ℂ n. Ann. Math. (2) 172(3), 1779–1840 (2011)
Pila, J., Zannier, U.: Rational points in periodic analytic sets and the Manin-Mumford conjecture, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei(9). Mat. Appl. 19(2), 149–162 (2008)
Shoenfield, J.R.: Mathematical Logic. A. K. Peters (2001)
Srivastava, S.M.: A Course on Borel Sets, GTM 180. Springer, New York (1998)
Swan, R.G.: Tarski’s principle and the elimination of quantifiers (preprint)
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Srivastava, S.M. (2013). Model Theory. In: A Course on Mathematical Logic. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5746-6_5
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DOI: https://doi.org/10.1007/978-1-4614-5746-6_5
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