Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 (1992) 149–172. We consider the language L(Hω) with all Henkin quantifiers H n defined as follows: H nx 1... x ny 1... y n φ( x 1,..., x n , y 1,..., y n ) iff ∃ f 1... f n ∀ x 1. .. x n φ( x 1,..., x n , f 1( x 1), ..., f n ( x n )). We show that the theory of equality in L(Hω) is undecidable. The proof of this result goes by interpretation of the word problem for semigroups. Henkin quantifiers are strictly related to the function quantifiers F n defined as follows: F nx 1... x ny 1... y n φ( x 1,..., x n , y 1,..., y n ) iff ∃ f∀ x 1... x n φ( x 1,..., x n , f( x 1),..., f( x n )). In contrast with the first result we show that the theory of equality with all quantifiers F n is decidable. We also consider decidability problems for other theories in languages L(F 2) and L(H 2).