Definability of Total Objects in PCF and Related Calculi
We let PCF be Plotkin’s  calculus based on Scott’s 10, 11 LCF, and we consider the standard case with base types for the natural numbers and for the Booleans. We consider the standard interpretation using algebraic domains. Plotkin  showed that a finite object in general will not be definable, and isolated two nondeterministic constants PAR and ∃ ω such that each computable object is definable in PCF + PAR + ∃ ω .
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