Geodesic
Reducibility of Monadic Equivalence Relations
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 842-854

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Each additive cut in the nonstandard natural numbers $\!{}^*{\mathbb N}$ induces the equivalence relation $\operatorname M_U$ on $\!{}^*{\mathbb N}$ defined as $x\operatorname M_Uy$ if $|x-y|\in U$. Such equivalence relations are said to be monadic. Reducibility between monadic equivalence relations is studied. The main result (Theorem 3.1) is that reducibility can be defined in terms of cofinality (or coinitiality) and a special parameter of a cut, called its width. Smoothness and the existence of transversals are also considered. The results obtained are similar to theorems of modern descriptive set theory on the reducibility of Borel equivalence relations.
Keywords: nonstandard analysis, additive cut of the hyperintegers, $\kappa$-determined set, $\kappa$-determined reducibility, width of a cut.
Mots-clés : monadic equivalence relation 
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     author = {V. G. Kanovei and V. A. Lyubetskii and M. Reeken},
     title = {Reducibility of {Monadic} {Equivalence} {Relations}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a3/}
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V. G. Kanovei; V. A. Lyubetskii; M. Reeken. Reducibility of Monadic Equivalence Relations. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 842-854. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a3/