Σ-Definability in Hereditarily Finite Superstructures and Computable Analysis

Springer Science and Business Media LLC - Tập 59 - Trang 763-767 - 2018
S. A. Aleksandrova1
1Novosibirsk State University, Novosibirsk, Russia

Tóm tắt

We construct a computable real function not Σ-definable in hereditarily finite superstructures over the extensions with decidable theory of the reals.

Tài liệu tham khảo

Weihrauch K., Computable Analysis. Texts in Theoretical Computer Science, An EATCS Series, Springer-Verlag, Berlin (2000). Ershov Yu. L., Definability and Computability, Consultants Bureau, New York and London (1996). Goncharov S. S. and Sviridenko D. I., “Σ-Programming,” Transl. II. Ser., Amer. Math. Soc., no. 142, 101–121 (1989). Korovina M. V., “Generalized computability over real functions,” Vychisl. Systemy, no. 133, 38–67 (1990). Korovina M. V., Generalized Computability over the Reals [Russian], Dis. Kand. Fiz.-Mat. Nauk, Inst. Mat., Novosibirsk (1996). Stukachev A. I., Ershov Yu. L., and Puzarenko V. G., “HF-Computability,” in: Computability in Context. Computation and Logic in the Real World, World Sci., Singapore, 2011, 169–242. Macintyre A. and Wilkie A., “On the decidability of the real exponential field,” in: Kreiseliana, A. K. Peters, Wellesley, 1996, 441–467.