The classical Heisenberg antiferromagnet on a triangular lattice with the single-ion anisotropy of the easy-axis type is theoretically investigated. The mean-field phase diagram in an external magnetic field is constructed. Three finite-temperature Berezinskii-Kosterlitz-Thouless transitions are found by the Monte Carlo simulations in zero field. The two upper transitions are related to the breaking of the discrete ${mathbb Z}_{6}$ symmetry group, while the lowest transition is associated with a quasi-long-range ordering of transverse components. The intermediate collinear phase between first and second transitions is the sliding phase predicted by J. V. Jose {it et al}. [Phys. Rev. B {bf 16}, 1217 (1977)].
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