Topology, forcing, and graph colourings

Key Points

• The aim is to explore how specific forcing notions can demonstrate the absence of countable colourings in certain graph classes.
• Introduce a family of forcing notions
• Analyze additive Borel classes
• Construct weakly minimal graphs for specific colourings
• Identified graphs lacking countable colourings of Borel class alpha
• Developed a framework using new forcing notions
• Demonstrated properties of weakly minimal graphs

Abstract