In programming language semantics, a relation between two models of a programming language is admissible when it is well-behaved with respect to recursion - in a domain-theoretic sense.
Suppose we have partial orders (D,⊑D) and (E,⊑E) which are complete. (This could be either chain-complete, or directed-complete, but we will choose chain-completeness here for simplicity.) Moreover, suppose they have least elements ⊥D and ⊥E respectively.
A relation R⊆D×E is admissible when
- it is strict, i.e. ⊥DR⊥E, and also
- it is chain-closed, i.e. if we have chains d0⊑Dd1⊑… and e0⊑Ee1⊑… with diRei for all i, then (⨆idi)R(⨆iei).