Finding the set of leaves for an unbounded tree is a nontrivial process in both the Weihrauch and reverse mathematics settings. Despite this, many combinatorial principles for trees are equivalent to their restrictions to trees with leaf sets. For example, let ${ \widehat{ \sf{ WF}}}$ denote the problem of choosing which trees in a sequence are well-founded, and let ${ { \sf{ PK}}}$ denote the problem of finding the perfect kernel of a tree. Let ${ \widehat{ \sf{ WF}}}_L$ and ${ { \sf{ PK}}}_L$ denote the restrictions of these principles to trees with leaf sets. Then ${ \widehat{ \sf{ WF}}}$, ${ \widehat{ \sf{ WF}}}_L$, ${ { \sf{ PK}}}$, and ${ { \sf{ PK}}}_L$ are all equivalent to ${ \Pi^1_1 { \rm -} { \sf{ CA}}_0}$ over ${ { \sf{ RCA}}_0}$, and all strongly Weihrauch equivalent.
Categories: math.LO