. "Any process that activates or increases the frequency, rate or extent of axial mesoderm cell fate determination." . . . "positive regulation of axial mesodermal cell fate determination" . "activation of axial mesodermal cell fate determination" . "stimulation of axial mesodermal cell fate determination" . "up regulation of axial mesodermal cell fate determination" . "up-regulation of axial mesodermal cell fate determination" . "upregulation of axial mesodermal cell fate determination" . .