On the semigroup of injective monoid endomorphisms of the monoid BωF³ with a three element family F³ of inductive nonempty subsets of ω

We describe injective monoid endomorphisms of the semigroup BωF³ with a three element family F³ of inductive nonempty subsets of ω. Also, we show that the monoid End_*¹(BωF) of all injective endomorphisms of the semigroup BωF³ is isomorphic to the multiplicative semigroup of positive integers.