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Sib. J. Pure and Appl. Math., 2018, Volume 18, Issue 1, Pages 3–10 (Mi vngu459)  

On $\Sigma$-definability of hereditarily finite and list superstructures

S. A. Aleksandrova

Novosibirsk State University

Abstract: This work is concerned with properties of hereditarily finite superstructures $\mathbb{HF}(\mathfrak{M})$ and hereditarily finite list superstructures $\mathbb{HW}(\mathfrak{M})$. The main result states that any relation $\Sigma$-definable in a hereditarily finite superstructure $\mathbb{HF}(\mathfrak{M})$ can also be defined by $\Sigma$-formula in a hereditarily finite list superstructure $\mathbb{HW}(\mathfrak{M})$ and vice versa.

Keywords: computability, $\Sigma$-definability, $\Sigma$-definable structure, hereditarily finite superstructure, hereditarily finite list superstructure.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-8648.2016.1


DOI: https://doi.org/10.17377/PAM.2018.18.1

Full text: PDF file (132 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 510.5
Received: 08.12.2017

Citation: S. A. Aleksandrova, “On $\Sigma$-definability of hereditarily finite and list superstructures”, Sib. J. Pure and Appl. Math., 18:1 (2018), 3–10

Citation in format AMSBIB
\Bibitem{Ale18}
\by S.~A.~Aleksandrova
\paper On $\Sigma$-definability of hereditarily finite and list superstructures
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 1
\pages 3--10
\mathnet{http://mi.mathnet.ru/vngu459}
\crossref{https://doi.org/10.17377/PAM.2018.18.1}


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