Uniformization in Superstructures Over Some Extensions of ℝ
Tóm tắt
The uniformization theorem for Σ-predicates in a hereditarily finite superstructure over the real exponential field proved in [1] is generalized to the case of an arbitrary Σ- predicate P ⊆ ℍ
$$ \mathbb{W} $$
(ℝ
exp
) ×ℍ
$$ \mathbb{W} $$
(ℝ
exp
).
Tài liệu tham khảo
S. A. Aleksandrova, “The uniformization problem for Σ-predicates in a hereditarily finite list superstructure over the real exponential field,” Algebra and Logic, 53, No. 1, 1–8 (2014).
S. S. Goncharov and D. I. Sviridenko, “Σ-programming,” Vych. Syst., 107, 3–29 (1985).
A. J. Wilkie, “Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function,” J. Am. Math. Soc., 9, No. 4, 1051–1094 (1996).
A. G. Khovanskii, “On a class of systems of transcendental equations,” Dokl. Akad. Nauk SSSR, 255, No. 4, 804–807 (1980).
A. Macintyre and A. Wilkie, “On the decidability of the real exponential field,” in Kreiseliana: About and around Georg Kreisel, P. Odifreddi (ed.), A K Peters, Wellesley, MA (1996), pp. 441–467.
Yu. L. Ershov, Definability and Computability, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1996).
M. V. Korovina, “Generalized computability of functions on real numbers,” Vych. Sist., 133, 38–67 (1990).
A. Gabrielov and N. Vorobjov, “Complexity of cylindrical decompositions of sub-Pfaffian sets,” J. Pure Appl. Alg., 164, Nos. 1/2, 179–197 (2001).
