# The ICICS/CS Reading Room

## UBC CS TR-84-04 Summary

- No on-line copy of this technical report is available.

- Classes of Numeration Models of $\lambda$-Calculus, April 1984 K and Akira a
In [4] the reflexive structures in the category of numeration were studied. It
was shown that every numerated reflexive set forms a ``numeration model of
$\lambda$-calculus''. In this short note we formalize the concept of numeration models of
$\lambda$-calculus, and study several interesting subclasses. Even though the class of
numeration models does not coincide with the class of numerated reflexive sets,
we can show that the class of numeration models with ``$\lambda$-definability'' property
is equivalent to the class of numerated reflexive sets with ``$\lambda$-representability''
property. Through this we observe relation between $\lambda$-definability and acceptability
of numerations discussed in [5].

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