Two hypergraph theorems equivalent to ${\rm BPI}$.
Robert H. Cowen · Notre Dame Journal of Formal Logic · 1990
Techniques originally developed for establishing NP-Completeness are adapted to prove that two compactness theorems concerning hypergraphs are equivalent to the Prime Ideal Theorem for Boolean algebras (BPI).In addition, some possible connections between NP-Completeness and BPI are explored. Theorem 13-SAT^BPI.