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Complementary pair of quasi-antiorders

Crvenkovic S., Mitrovic M., Romano D. A.

Reports on Mathematical Logic

2010

Vol. 45

135-142

The aims of the present paper are to introduction and investigate of notions of complementary pairs of quasi-antiorders and half-space quasi-antiorder on a given set. For a pair alfa and beta of quasi-antiorders on a given set A we say that they are complementary pair if alfa union beta =not equal to=A and alfa intersection beta = empty set. In that case, alfa (and beta ) is called half-space on A. Assertion, if alfa is a half-space quasi-antiorder on A, then the induced anti-order theta on A/(alfa union alfa -1) is a half-space too, is the main result of this paper.