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On Σ-rigid presentations of the real order

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Abstract

For arbitrary tuples of real parameters \(\bar p\), we prove the existence and effective infiniteness of the class of the linear orders on ℝ of type 〈ℝ,<〉 which are Σ-definable over \(\mathbb{H}\mathbb{F}(\mathbb{R})\) with parameters \(\bar p\) and have no nontrivial Σ-definable self-embeddings with parameters \(\bar p\).

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References

  1. Barwise J., Admissible Sets and Structures, Springer-Verlag, Berlin, Göttingen, and Heidelberg (1975).

    Book  MATH  Google Scholar 

  2. Ershov Yu. L., “Σ-Definability of algebraic structures,” in: Handbook of Recursive Mathematics. Vol. 1. Recursive Model Theory, Elsevier Sci. B. V., Amsterdam, 1998, pp. 235–260 (Stud. Logic Found. Math.; 138).

    Chapter  Google Scholar 

  3. Ershov Yu. L., Puzarenko V. G., and Stukachev A. I., “HF-Computability,” in: Computability in Context: Computation and Logic in the Real World, S. B. Cooper and A. Sorbi (eds.), Imperial College Press/World Sci., London, 2011, pp. 169–242.

    Chapter  Google Scholar 

  4. Morozov A. S., “Some presentations of the real number field,” Algebra and Logic, 51, No. 1, 66–88 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  5. Morozov A. S., “Nonpresentability of the semigroup ωω over HF(R),” Siberian Math. J., 55, No. 1, 125–131 (2014).

    Article  Google Scholar 

  6. Morozov A. S., “On Σ-presentations of the real order,” Algebra and Logic (to be published).

  7. Ershov Yu. L., Definability and Computability, Consultants Bureau, New York and London (1996).

    Google Scholar 

  8. Tarski A., A Decision Method for Elementary Algebra and Geometry, Rand Corporation, Santa Monica (1957).

    Google Scholar 

  9. Marker D., Model Theory: An Introduction, Springer-Verlag, New York (2002) (Graduate Texts in Mathematics; 217).

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. S. Morozov

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  1. A. S. Morozov
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Correspondence to A. S. Morozov.

Additional information

Original Russian Text Copyright © 2014 Morozov A.S.

The author was supported by the Russian Foundation for Basic Research (Grant 14-01-00376) and the Leading Scientific Schools of the Russian Federation (Grant NSh-860.2014.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 562–572, May–June, 2014.

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Morozov, A.S. On Σ-rigid presentations of the real order. Sib Math J 55, 457–464 (2014). https://doi.org/10.1134/S0037446614030070

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  • DOI: https://doi.org/10.1134/S0037446614030070

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