Geodesic
$\Sigma$-uniform structures and $\Sigma$-functions.~I
Algebra i logika, Tome 50 (2011) no. 5, pp. 659-684.

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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. 
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A. N. Khisamiev. $\Sigma$-uniform structures and $\Sigma$-functions.~I. Algebra i logika, Tome 50 (2011) no. 5, pp. 659-684. http://geodesic.mathdoc.fr/item/AL_2011_50_5_a4/

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