Order structures and generalisations of Szpilrajn's theorem

Relational structures of the form (X, R1,R2), with R1 ⫅R2 ⫅ X × X, R1 being a poset interpreted as causality, R2 being interpreted as ‘not later than’ or ‘weak causality’ relation, are considered. Szpilrajn's theorem that each poset is the intersection of its total extensions is generalised to such structures; the interpretation and applications of the results obtained are discussed.