arithmetical hierarchy is a proper hierarchy
More significant is the proof that all containments are proper. First, let and be universal for -ary relations. Then is obviously . But suppose . Then , so . Since is universal, ther is some such that , and therefore . This is clearly a contradiction, so and .
In addition the recursive join of and , defined by
|Title||arithmetical hierarchy is a proper hierarchy|
|Date of creation||2013-03-22 12:55:14|
|Last modified on||2013-03-22 12:55:14|
|Last modified by||Henry (455)|