Comments (4)
I think your second paragraph is right. There are no "universe variables" in the formal system of the book.
from book.
I'm not sure what you mean by "uniformly" introducing functions. There are certainly better ways to set up a theory of universes if you're going to implement it in a proof assistant, but I believe that in the Book the subscripts on universes are literally metatheoretic natural numbers, so they do have least upper bounds. The treatment of universes in the definition of things like function-types is, well, ambiguous, because it uses typical ambiguity, but I think the intent was that all types involved live in the same universe.
from book.
Thanks for the comment. To give a concrete example: if we have
Or maybe what I'm misunderstanding is the use of "variable indices", and a theorem involving them as in the book was meant to be a theorem schema involving every (metatheoretical) natural number.
That's what I meant by "uniformly" defining functions, doing so for every pair of variable indices, not just a pair of concrete ones. To be clear, I understand that metatheoretically we can show that we can do so for every concrete pair (and therefore all pairs), but, at least to me, one of the advantages of DTT was being able to internalize these sort of things through dependent protducts.
from book.
Thanks!
from book.
Related Issues (20)
- 自动驾驶更新笔记 Autopilot Updating Notes HOT 1
- Augment assumptions for Thm 5.4.4, 5.4.5, and 5.4.7 HOT 19
- Typos in proof of Lemma 10.3.12 HOT 5
- Use parentheses in the proof of Lemma 2.1.4(iii) HOT 3
- CI problem: "dubious ownership" HOT 1
- Provided Hashes in errata.pdf Not Found HOT 2
- Errata PDF unreadable
- Corollary 8.8.5 HOT 4
- Lemma 8.5.9 is missing a label
- Nightly builds pdfs are dead links HOT 8
- Exercise 7.3 could be made stronger
- Indexing of maps in fiber and exact sequences HOT 3
- proof-theoretic consistency in the introduction HOT 6
- cardinal numbers in the introduction HOT 5
- real numbers in the introduction HOT 7
- Switch to using truncated logic as default in the book HOT 2
- max and sup HOT 9
- Exercise 11.6 seems to need WLPO not LPO HOT 3
- Incorrect diagram for Example 8.7.16 HOT 1
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from book.