Alexander Kharazishvili

On Mutually Coherent Enumerations of Countable Sets

The notion of compatibility of enumerations of countable (in particular, finite) sets is introduced and investigated. Some purely combinatorial problems connected with this notion are considered and several conditions are presented for the existence of mutually coherent enumerations of all members of a given family of countable sets.

Mutually coherent enumerations, Latin square, initial partial selector, point-finite family of sets, admissible family of sets.

MSC 2000: 03E05, 03E20, 05A05, 05A99