Algebraic properties and dismantlability of finite posets Original Research Article

We show that every finite connected poset which admits certain operations such as Gumm or Jónsson operations, or a near unanimity function is dismantlable. This result is used to prove that a finite poset admits Gumm operations if and only if it admits a near unanimity function. Finite connected posets satisfying these equivalent conditions are characterized by the property that their idempotent subalgebras are dismantlable. As a consequence of these results we obtain that the problem of determining if a finite poset admits a near unanimity function is decidable.