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$\Pi ^0_1$ CLASSES
We study for each computably bounded 
$\Pi ^0_1$ class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect 
$\Pi ^0_1$ class where all c.e. members have degree a. We also show that every 
$\Pi ^0_1$ set of c.e. indices is realized in some perfect 
$\Pi ^0_1$ class, and classify the sets of c.e. degrees which can be realized in some 
$\Pi ^0_1$ class as exactly those with a computable representation.
We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are 
${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed 
${\operatorname {\mathrm {low}}}_n$ cuppable for any n, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the 
${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.
