Morasses, square and forcing axioms (Q1923568)

The paper discusses various relationships between morasses, square and forcing axioms. Under \(V=L\) there is a \((\kappa,1)\)-simplified morass with small limits if and only if there is a \((\kappa,1)\)-simplified morass with simple limits. Moreover \((\kappa,1)\)-simplified morasses with simple paths correspond to \(\kappa\)-closed forcing axioms, with small limits corresponding to \(\kappa\)-thin-directed closed forcing axioms and with continuous paths corresponding to strongly strategic forcing axioms.