I would like to understand the following quote, from a [paper](https://arxiv.org/abs/1108.4223) by Joel Hamkins:
> Adherents of the universe view often point to the increasingly stable consequences of the large cardinal hierarchy, particularly in the realm of projective sets of reals with its attractive determinacy and regularity features, as well as the forcing-absoluteness properties for L(R), as evidence that we are on the right track towards the final answers to these set theoretical questions.
1. What is the large cardinal hierarchy?
2. What are its stable consequences?
3. What are projective sets?
4. What are determinacy and regularity features?
5. What is L(R)?
Julius H.
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2024-02-10T15:35:55Z (11 months ago)