Activity for Hernán Ibarra Mejia
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #296026 |
@#117674 Anyways, these philosophical questions are only rethorical; you've already clarified the situation for me. I will mark this answer as accepted. (more) |
— | 5 months ago |
| Comment | Post #296026 |
@#117674 Wow, I had no idea that ZFC is not known to be arithmetically sound; I find this very disturbing. While one can argue empirically for the consistency of ZFC, I have not seen any convincing reasons as to why ZFC should be arithmetically sound. I found some interesting literature in this d... (more) |
— | 5 months ago |
| Comment | Post #296026 |
Thanks, this seems to be exactly what I'm looking for. I am convinced that provability is in $\Sigma^0_1$ ("there exists a finite string of symbols such that they form a proof"). But something is still unclear to me. **Do we know whether ZFC is $\Sigma^0_1$-sound?**
If it helps, I'm taking the... (more) |
— | 5 months ago |
| Edit | Post #296016 |
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— | 5 months ago |
| Edit | Post #296016 |
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— | 5 months ago |
| Edit | Post #296016 | Initial revision | — | 5 months ago |
| Question | — |
When is proof of provability a proof? I am writing some notes on mathematical logic and I hit upon something I never really understood. I am pretty sure my question is elementary; nevertheless, I would appreciate help clearing my confusion. We start with a bare-bones metatheory, enough to manipulate and reason about finite strings... (more) |
— | 5 months ago |
| Comment | Post #295858 |
And thank you for another great reference. These posts will be a pleaseant afternoon read. (more) |
— | 6 months ago |
| Comment | Post #295859 |
Note also that $X\times X \cong X$ with the projections being the identity map. This appeared earlier in the book—didn't think it could be applied directly. Great answer! (more) |
— | 6 months ago |
| Comment | Post #295858 |
Thanks for the Reyes et. al reference, it looks interesting. Do you know how it compares with Lawvere & Rosebrugh's *Sets for Mathematics*? I'm looking to do more reading on topos (with an eye towards logic) after *Conceptual Mathematics*. (more) |
— | 6 months ago |
| Edit | Post #295855 | Initial revision | — | 6 months ago |
| Question | — |
Prove that if $X^X$ is a terminal object then $X \to \mathbf{1}$ is a monomorphism I want to know how to solve the following exercise in the textbook Conceptual Mathematics by Lawvere [Session 31, Exercise 2]. > Let $X$ be an object in a cartesian closed category. Show that the following > two properties are equivalent: > > 1) $X \to \mathbf{1}$ is a monomorphism; > 2) ... (more) |
— | 6 months ago |