I was reading through the Wikipedia article on the Continuum Hypothesis and I was unclear why it couldn't be handled like the Parallel Postulate of Euclid?
Is there any reason to believe that there must be an answer to this question? If it turns out that the Continuum Hypothesis is undecidable would that not open up at least two different branches of mathematical systems: one system where the Continuum Hypothesis is true and one where it is false?
Would it be accurate to say that the Parallel Postulate of Euclid is undecidable since a logically consistent geometry can be built from assuming it is true or assuming it is false?
Sorry if these questions are dumb. I'm trying to get my head around the continuum hypothesis, decidability, and its relation to non-Euclidean Geometry systems if there is any relationship.