Abstract (EN)

Necessary and suffcient conditions under which semiorders on uncountable sets can be represented by a real-valued function and a constant threshold are known. We show that the proof strategy that we used for constructing representations in the case of denumerable semiorders can be adapted to the uncountable case. We use it to give an alternative proof of the existence of strict unit representations. A direct adaptation of the same strategy allows us to prove a characterization of the semiorders that admit a nonstrict representation.