An essay on model theory

• Autorzy: Ludomir Newelski
• Języki publikacji: EN

Abstrakty

EN

Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.

Słowa kluczowe

EN

stability theory; geometric model theory; 03-02

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 398-410

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Ludomir Newelski

• University of Wroclaw

Bibliografia

• [1] [Ba] J.T. Baldwin: Fundamentals of Stability Theory, Springer, Berlin, 1988.
• [2] [Bu] S. Buechler: “Vaught conjecture for superstable theories of finite rank”, (1993), preprint.
• [3] [CS] G. Cherlin and S. Shelah: “Superstable fields and groups”, Ann. Math. Logic, Vol. 18, (1980), pp. 227–270. http://dx.doi.org/10.1016/0003-4843(80)90006-6
• [4] [CR] H.H. Crapo and G.C. Pota: On the foundations of combinatorial theory: combinatorial geometries, MIT Press, Cambridge (Mass.), 1970.
• [5] [D] L. van den Dries: Tame topology and o-minimal structures, London Math. Soc. Lecture Notes Series 248, Cambridge Univ. Press, Cambridge, 1998.
• [6] [Ho] W. Hodges: Model theory, Cambridge Univ. Press, Cambridge, 1993.
• [7] [H1] E. Hrushovski: Contributions to model theory, Ph.D. thesis, Univ. of California at Berkeley, Berkeley, 1996.
• [8] [H2] E. Hrushovski: “A new strongly minimal set”, Ann. Pure Appl. Logic, Vol. 50, (1990), pp. 117–138. http://dx.doi.org/10.1016/0168-0072(90)90046-5
• [9] [CK] C.C. Chang and H.J. Keisler: Model Theory, 3rd Ed., North Holland, Amsterdam, 1990.
• [10] [L] D. Lascar: “Why some people are excited by Vaught’s conjecture”, J. Symb. Logic, Vol. 50, (1985), pp. 973–982. http://dx.doi.org/10.2307/2273984
• [11] [Mc] A. Macintyre: “On N 1-categorical theories of fields”, Fund. Math., Vol. 71, (1971), pp. 1–25.
• [12] [Ma] D. Marker: Model theory. An introduction, Grad. Texts in Math., Springer, New York, 2002.
• [13] [Mo] M. Morley: “Categoricity in power”, Trans. AMS, Vol. 114, (1964), pp. 514–538. http://dx.doi.org/10.2307/1994188
• [14] [NPi] A. Nesin and A. Pillay: “Some model theory of compact Lie groups”, Trans. AMS, Vol. 326, (1991), pp. 453–463. http://dx.doi.org/10.2307/2001873
• [15] [Ne1] L. Newelski: “A proof of Saffe’s conjecture”, Fund. Math., Vol. 134, (1990), pp. 143–155.
• [16] [Ne2] L. Newelski: “Meager forking and m-independence”, Proc. Int. Congress of Math., Berlin, 1998, Doc. Math., Extra Vol. II, (1998), pp. 33–42.
• [17] [Ne3] L. Newelski: “m-normal theories”, Fund. Math., Vol. 170, (2001), pp. 141–163. http://dx.doi.org/10.4064/fm170-1-9
• [18] [Ne4] L. Newelski: “Small profinite groups”, J. Symb. Logic, Vol. 66, (2001), pp. 859–872. http://dx.doi.org/10.2307/2695049
• [19] [Ne5] L. Newelski: “Small profinite structures”, Trans. AMS, Vol. 354, (2002), pp. 925–943. http://dx.doi.org/10.1090/S0002-9947-01-02854-9
• [20] [Ne6] L. Newelski: “The diameter of a Lascar strong type”, Fund. Math., Vol. 176, (2003), pp. 157–170.
• [21] [NPe] L. Newelski and M. Petrykowski: Coverings of groups and types, manuscript, 2003.
• [22] [Pi1] A. Pillay: Geometric Model Theory, Clarendon Press, Oxford, 1996.
• [23] [Pi2] A. Pillay: “Some model theory of compact complex spaces”, In: Hilbert’s tenth problem: relations with arithmetic and algebraic geometry. Ghent, 1999, Contemp. Math., Vol. 270, pp. 323–338.
• [24] [Pi3] A. Pillay: “Model-theoretic consequences of a theorem of Campana and Fujiki”, Fund. Math., Vol. 174, (2002), pp. 187–192.
• [25] [Po] B. Poizat: Groupes stables, Nur Al-Mantiq Wal-Ma’rifah, Villeurbane, France, 1985.
• [26] [Sa] G. Sacks: Saturated Model Theory, Benjamin, Reading, 1972.
• [27] [Sc] T. Scanlon: “The abc theorem for commutative algebraic groups in characteristic p”, Int. Math. Res. Notices, No. 18, (1997), pp. 881–898. http://dx.doi.org/10.1155/S1073792897000573
• [28] [Sh] S. Shelah: Classification Theory and the number of non-isomorphic models, 2nd Ed., North Holland, Amsterdam, 1990.
• [29] [SHM] S. Shelah, L. Harrington, M. Makkai: “A proof of Vaught’s conjecture for ω-stable theories”, Israel J. Math., Vol. 49, (1984), pp. 181–238.
• [30] [Wa] F.O. Wagner: Simple Theories, Kluwer, Dodrecht, 2000.

Identyfikatory

DOI

10.2478/BF02475218