I know that if you try and make the theory
$$\lambda\beta+\{s = t\ |\text{ s, t are terms without }\lambda\beta\text{ normal forms}\}$$
then that theory becomes inconsistent. Are two terms where one is without a $\lambda\beta$ normal form also unconvertible in $\lambda\beta$, ie can it ever be true that $\lambda\beta \vdash s=t$ if $s$ dosen't have a normal form?
s
that is not normalisable and any termt
, is it always the case that you can never equate them using the rules of lambda beta? $\endgroup$ – Callum Rogers Nov 12 '12 at 17:49