Sandwiches of ages Original Research Article

The age of a relational structure R is the set View the MathML source of finite restrictions of R considered up to isomorphism. R. Fraı̈ssé, who introduced this notion, showed that ages coincide with nonempty ideals of the poset consisting of finite relational structures, considered up to isomorphism and ordered by embeddability. Here, given two ages View the MathML source, we study the poset View the MathML source consisting of ages View the MathML source in sandwich between View the MathML source and View the MathML source. Among other things we show that if View the MathML source is infinite then it contains an infinite chain.