This article is cited in 6 papers

On a universal $\Sigma$-function over a tree

A. N. Khisamiev

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

Abstract: We obtain a sufficient condition for the absence of any universal $\Sigma$-function in an admissible set (a hereditarily finite admissible set). We construct a tree $T$ of height 4 such that no universal $\Sigma$-function exists in the hereditarily finite admissible set $\mathbb{HF}(T)$ over $T$.

Keywords: admissible set, $\Sigma$-function, universal $\Sigma$-function, hereditarily finite admissible set, tree.

UDC: 512.540+510.5

Received: 30.05.2011

 English version: Siberian Mathematical Journal, 2012, 53:3, 551–553

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