Quantifier hierarchies over the first-order definable tree languages (Q1924423)

Notions as star-freeness and aperiodicity have been transferred to tree languages but not many results still hold true (for example, the class of first-order definable tree languages is strictly included in the class of star-free languages). An alternative quantifier hierarchy over the first-order definable tree languages is presented. It is a generalization of the ``classical'' one (for first-order definable word languages) and uses Boolean operations and product (concatenation with respect to ``special'' trees).