A note on noninterpretability in o-minimal structures

• Autorzy: Ricardo Bianconi
• Języki publikacji: EN

Abstrakty

EN

We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.

Kategorie tematyczne

• 06F99: None of the above, but in this section
• 03C45: Classification theory, stability and related concepts
• 03C40: Interpolation, preservation, definability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 1
• Strony: 19-22

Daty

wydano

1998

otrzymano

1996-08-22

poprawiono

1997-12-07

Twórcy

autor

Ricardo Bianconi

• IMEUSP, Caixa Postal 66281, CEP 05315-970, São Paulo, SP, Brazil

Bibliografia

• [1] L. van den Dries, Tame Topology and O-minimal Structures, London Math. Soc. Lecture Note Ser. 248, Cambridge Univ. Press, 1998.
• [2] J. Knight, A. Pillay and C. Steinhorn, Definable sets in ordered structures II, Trans. Amer. Math. Soc. 295 (1986), 593-605.
• [3] J. Krajíček, Some theorems on the lattice of local interpretability types, Z. Logik Grundlagen Math. 31 (1985), 449-460.
• [4] J. Mycielski, P. Pudlák and A. Stern, A lattice of chapters of mathematics (interpretations between theorems), Mem. Amer. Math. Soc. 426 (1990).
• [5] A. Pillay, Some remarks on definable equivalence relations in o-minimal structures, J. Symbolic Logic 51 (1986), 709-714.
• [6] A. Pillay and C. Steinhorn, Discrete o-minimal structures, Ann. Pure Appl. Logic 34 (1987), 275-289.
• [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures I, Trans. Amer. Math. Soc. 295 (1986), 565-592.
• [8] A. Pillay and C. Steinhorn, Definable sets in ordered structures III, ibid. 309 (1988), 469-476.
• [9] S. Świerczkowski, Order with successors is not interpretable in RCF, Fund. Math. 143 (1993), 281-285.