MENAS'S CONJECTURE REVISITED

In an article published in 1974, Menas conjectured that any stationary subset of P ( kappa )(lambda) can be split in lambda(kappa) many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on P ( kappa )(lambda). In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we keep weakening this new assertion until, building on the work of Usuba, we hit something we can prove.