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Semiorders with separability properties

2012; Elsevier BV; Volume: 56; Issue: 6 Linguagem: Inglês

10.1016/j.jmp.2013.01.003

1096-0880

Juan C. Candeal, Asier Estevan, Javier Gutiérrez García, Esteban Induráin,

Advanced Algebra and Logic

We analyze different separability conditions that characterize the numerical representability of semiorders through a real-valued function and a strictly positive threshold. Any necessary and sufficient condition for the numerical representability of an interval order by means of two real-valued functions is proved to also characterize the Scott–Suppes representability of semiorders provided that a key additional condition of regularity with respect to sequences holds.