This article is cited in 7 papers

$\Sigma$-uniform structures and $\Sigma$-functions. I

A. N. Khisamiev

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: The concept of a $\Sigma$-uniform structure is introduced. A condition is derived which is necessary and sufficient for a universal $\Sigma$-function to exist in a hereditarily finite admissible set over a $\Sigma$-uniform structure.

Keywords: hereditarily finite admissible set, $\Sigma$-definability, universal $\Sigma$-function, $\Sigma$-uniform structure.

UDC: 512.540+510.5

Received: 24.11.2010
Revised: 05.06.2011

 English version: Algebra and Logic, 2011, 50:5, 447–465

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