Set Theory of The Real Line
There are many cardinal invariants of the real line, connected with measure theory and statements related to the Baire category theorem whose exact values are independent of ZFC (in a stronger sense than that CH is in ZFC. While nontrivial relations can be proved between them, most cardinal invariants can be any regular cardinal between ℵ1 and 2ℵ0). This is a major area of study in set theoretic real analysis. MA has a tendency to set most interesting cardinal invariants equal to 2ℵ0.
Read more about this topic: List Of Statements Undecidable In ZFC
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