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Cameo of a Consummate Computabilist Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Computable Model Theory over the Reals

Author : Andrey S. Morozov

Published in: Computability and Complexity

Publisher: Springer International Publishing

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Abstract

This paper is a survey of results together with a list of open questions on \(\Sigma \)–definability of structures over \(\mathbb {HF}(\mathbb {R})\), the hereditarily finite superstructure over the ordered field of the real numbers.

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previous chapter On Constructive Nilpotent Groups
next chapter The Lattice of Computably Enumerable Vector Spaces
Literature
1.
Morozov, A.S., Korovina, M.V.: On \(\Sigma \)-definability of countable structures over real numbers, complex numbers, and quaternions. Algebra Logic 47(3), 193–209 (2008)MathSciNetCrossRefMATH
2.
3.
Ershov, Y.L.: Definability and Computability. Plenum Publ. Co., New York (1996)MATH
4.
Ershov, Y.L.: \(\Sigma \)-definability of algebraic structures. In: Studies in Logic and Foundations of Mathematics, vol. 1, pp. 235–260. Elsevier, Amsterdam (1998)
5.
Korovina, M.V.: Generalized computability of functions on the reals. Vychislitel’nye Systemi (Computing Systems) 133, 38–68 (1990). In RussianMathSciNet
6.
7.
8.
Morozov, A.S.: One-dimensional \(\Sigma \)-presentations of structures over \(\mathbb{HF}{\mathbb{R}}\). In: Geschke, P.S.S., Löwe, B. (eds.) Infinity, Computability, and Metamathematics, Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch. Tributes Series, vol. 23, pp. 285–298. College Publications, London (2014)
9.
10.
Morozov, A.S.: A sufficient condition for nonpresentability of structures in hereditarily finite superstructures. Algebra Logic 55, 242–251 (2016)CrossRef
11.
Morozov, A.S.: Nonpresentability of some structures of analysis in hereditarily finite superstructures. Algebra Logic (2017, to appear)
12.
Korovina, M.V., Kudinov, O.V.: Positive predicate structures for continuous data. Math. Struct. Comput. Sci. 25(Special Issue 08), 1669–1684 (2015)MathSciNetCrossRefMATH
13.
Ershov, Y.L., Goncharov, S.S.: Constructive Models. Siberian School of Algebra and Logic. Kluwer Academic/Plenum, New York (2000)CrossRefMATH
14.
Tarski, A.: A Decision Method for Elementary Algebra and Geometry. The Rand Corporation, Santa Monica (1957)MATH
15.
16.
Ershov, Y.L., Puzarenko, V.G., Stukachev, A.I.: \(\mathbb{HF}\)-Computability. In: Cooper, S.B., Andrea, S. (eds.) Computability in Context. Computation and Logic in the Real World, pp. 169–242. Imperial College Press, London (2011)
Metadata
Title
Computable Model Theory over the Reals
Author
Andrey S. Morozov
Copyright Year
2017
Book
Computability and Complexity

Print ISBN: 978-3-319-50061-4

Electronic ISBN: 978-3-319-50062-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-50062-1_22

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