S. A. Aleksandrova, “On <nobr>$\Sigma$</nobr>-definability of hereditarily finite and list superstructures”, Sib. J. Pure and Appl. Math., 2018, Volume 18, Issue 1,Pages <nobr>3

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

S. A. Aleksandrova

Novosibirsk State University, 1, Pirogova St., Novosibirsk 630090, Russia

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.

UDC: 510.5

Received: 08.12.2017

DOI: 10.17377/PAM.2018.18.1