This thesis investigates several forcing axioms for sigma-closed posets with certain chain conditions at omega_2 and studies their consequences for combinatorial objects of cardinality omega_2. More precisely, we show that under an axiom developed by Shelah [33], all countably saturated omega_2-Countryman lines are minimal, all omega_2- Lipschitz trees are irreducible, and there are no maximal omega_2-Aronszajn trees. We will also prove the inconsistency of the forcing axiom for well-met, omega_2-Knaster, sigma-closed posets. This inconsistency result was suggested by Todorcevic.