We investigate the domain-theoretic denotational semantics of a CPS calculus with fresh name declaration. This is the target of a fully abstract CPS translation from the nu-calculus with first-class continuations. We describe a notion of ``FM-categorical'' model for our calculus, with a simple interpretation of name generation due to Shinwell and Pitts. We show that full abstraction fails (at order two) in the simplest instance of such a model (FM-cpos) because of the presence of parallel elements. Accordingly, we define a sequential model --- FM-biorders, based on ``bistable FM-bicpos'' and bistable functions --- and prove that it is fully abstract up to order four (our main result), but that full abstraction fails at order five.

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    title = "Sequentiality and the CPS semantics of fresh names",
    booktitle = "Proceedings of MFPS '07",
    series = "ENTCS",
    publisher = "Elsevier",
    number = 173,
    pages = "203 --219",
    year = 2007}