Geodesic
Limitwise monotonic reducibility on sets and on pairs of sets
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 97-101

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We study limitwise monotonic sets and pairs of sets. We investigate the properties of limitwise monotonic reducibility between sets and pairs of sets defined in terms of $\Sigma$-reducibility corresponding to initial segment of sets. In addition, we obtain a description of $\Sigma$-reducibility of families of a special form in terms of $lm$-reducibility. At the same time we show the relationship of concepts of $lm$-reducibility and $\Sigma$-reducibility between the pairs of sets.
Keywords: computable functions, $\Sigma$-reducibility, $\Sigma^0_2$-sets, limitwise monotonic function, limitwise monotonic sets, limitwise monotonic reducibility, pair of sets, family of subsets of natural numbers. 
@article{IVM_2016_3_a10,
     author = {D. Kh. Zainetdinov},
     title = {Limitwise monotonic reducibility on sets and on pairs of sets},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {97--101},
     publisher = {mathdoc},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_3_a10/}
}
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D. Kh. Zainetdinov. Limitwise monotonic reducibility on sets and on pairs of sets. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 97-101. http://geodesic.mathdoc.fr/item/IVM_2016_3_a10/