A note on Isomorphism theorems for semigroups of order-preserving   transformations with restricted range
  Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \cite{FHQS}. In this paper, we show a proof strategy to answer that question. 
Phichet Jitjankarn, Thitarie Rungratgasame
math.RA