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Sibirsk. Mat. Zh., 2014, Volume 55, Number 3, Pages 562–572 (Mi smj2553)  

This article is cited in 3 scientific papers (total in 3 papers)

On $\Sigma$-rigid presentations of the real order

A. S. Morozovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: For arbitrary tuples of real parameters $\bar p$, we prove the existence and effective infiniteness of the class of the linear orders on $\mathbb R$ of type $\langle\mathbb R,<\rangle$ which are $\Sigma$-definable over $\mathbb{HF(R)}$ with parameters $\bar p$ and have no nontrivial $\Sigma$-definable self-embeddings with parameters $\bar p$.

Keywords: $\Sigma$-definable model, computable model, computability, $\Sigma$-definability, admissible set, linear order.

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English version:
Siberian Mathematical Journal, 2014, 55:3, 457–464

Bibliographic databases:

UDC: 510.5
Received: 26.12.2012

Citation: A. S. Morozov, “On $\Sigma$-rigid presentations of the real order”, Sibirsk. Mat. Zh., 55:3 (2014), 562–572; Siberian Math. J., 55:3 (2014), 457–464

Citation in format AMSBIB
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\paper On $\Sigma$-rigid presentations of the real order
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\pages 457--464
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Morozov, “A sufficient condition for nonpresentability of structures in hereditarily finite superstructures”, Algebra and Logic, 55:3 (2016), 242–251  mathnet  crossref  crossref  isi
    2. A. S. Morozov, “Computable model theory over the reals”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. A. Day, M. Fellows, N. Greenberg, B. Khoussainov, A. Melnikov, F. Rosamond, Springer, 2017, 354–365  crossref  mathscinet  zmath  isi  scopus
    3. S. A. Aleksandrova, “O $\Sigma$-opredelimosti nasledstvenno konechnoi i spisochnoi nadstroek”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 3–10  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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