Geodesic
Universal computable enumerations of finite classes of families of total functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 96-100

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In the paper we introduce the notion of a computable enumeration of a class of families. We prove a criteria for the existence of uiversal computable enumerations of finite classes of computable families of total functions. In particular, we show that there is a finite computable class of families of total functions without universal computable enumerations.
Keywords: computable enumeration, universal enumeration, class of families, arithmetical enumeration. 
@article{IVM_2016_12_a10,
     author = {M. Kh. Faizrakhmanov},
     title = {Universal computable enumerations of finite classes of families of total functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {96--100},
     publisher = {mathdoc},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_12_a10/}
}
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M. Kh. Faizrakhmanov. Universal computable enumerations of finite classes of families of total functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 96-100. http://geodesic.mathdoc.fr/item/IVM_2016_12_a10/