We investigate the topological complexity of non Borel recognizable
tree languages with regard to the difference hierarchy of analytic sets. We
show that, for each integer n ⩾ 1, there is a D
_{ω^n}
(Σ
^1_1
)-complete
tree language L
_n
accepted by a (non deterministic) Muller tree automaton. On
the other hand, we prove that a tree language accepted by an unambiguous
Büchi tree automaton must be Borel. Then we consider the game tree
languages W
_{(ı,κ)}
, for Mostowski-Rabin indices (ıκ). We prove that
the D
_{ω^n}
(Σ
^1_1
)-complete tree languages L
_n
are Wadge reducible to the game tree
language W
_{(ı,κ)}
for κ−ı⩾ 2. In particular these languages
W
_{(ı,κ)}
are not in any class D
_{α}
(Σ
^1_1
)
for α<ω
^{ω}
.
