Sequentiality in bounded biorders

We study a notion of bounded stable biorder, showing that the monotone and stable functions on such biorders are sequential. We construct bounded biorder models of a range of sequential, higher-order functional calculi, including unary PCF, (typed and untyped) call-by-value and lazy lambda-calculi, and non-deterministic SPCF We prove universality and full abstraction results for these models by reduction to the case of unary PCF, for which we give a simple new argument to show that any order-extensional and sequential model is universal.