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5:46 AM
May 12 at 6:17, by Martin Sleziak
Two new tags and . They were both created in the same question - which does not have a top-level tag: Is diamond consistent with 2nd order PA?
The tag now contains four questions.
Q: Is diamond consistent with 2nd order PA?

Vladimir KanoveiIf $T$ is a theorem of ZF which says something only about reals, then one may want to prove $T$ using a theory like 2nd order PA or related theories like ZFC$^-$ or GBC$^-$ (minus accounts for the absence of the Power Set axiom). In many cases this goes through, sometimes rather straightforwardly...

Q: Is it consistent to have an infinite antitone sequence of elementary embeddings such that the involved models include iterated sharps?

Kristian BerryBackground essays (the material I've tried to understand in leading up to this question): Daghighi, et. al. [2014], "The foundation axiom and elementary self-embeddings of the universe." Dimonte [2017], "I0 and rank-into-rank axioms." To some extent, I've also tried to invoke Dougherty[92] in my...

Q: Why is an internal proof of consistency satisfactory for some systems?

student25I've only a shallow understanding of the relevant theory, but I don't understand how any internal proof of consistency is in any way satisfactory (even for systems that are so weak Gödel's incompleteness theorem doesn't apply). After all, suppose you've proven consistency from the axioms, both th...

Q: In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that PA is consistent?

JoeIt seems common amongst logicians to think of "truth" as being relative to a particular structure. Consider, for instance, the first-order theory of groups. The sentence $\forall x\forall y(x\cdot y=y\cdot x)$ is neither provable nor disprovable from the group axioms. However, rather than saying ...

yesterday, by Martin Sleziak
Tags with a single occurrence and no tag-wiki: main, meta
BTW the tag (created in the same question) is now at the top of the list with the tags prepared for pruning.
4 hours later…
10:21 AM
@MartinSleziak I removed , since, especially without tag info, it is likely to attract random geometry questions involving ellipses.
@MartinSleziak I removed , especially because "diamond" is also widely used in algebraic-geometry à la Scholtze. If a diamond tag is created, it should be more specific.
@MartinSleziak I guess should be removed. It is a quite broad tag in set theory. I think that tags that are in principle suitable for hundred/thousands of question but are only used for a few rare ones, are not useful.
10:36 AM
@YCor I do not have strong opinion either way.
The tag was created in May as you can see above - and nobody mentioned anything about this tag since then.
I have added it to one question - if the tag is going to be kept, it seems to be suitable for that question.
10:59 AM
@MartinSleziak to substantiate my claim: there are (search <<consistent [set-theory] is:question>>) 785 questions with the tag including the word "consistent"
11:09 AM
Here is a link to the search mentioned above - in case somebody wants to have a look.
1 hour later…
12:29 PM
Maybe some people see the tag system on MO as something that is already beyond saving - if that's the case, any discussions about tags are basically irrelevant.
1 hour later…
1:29 PM
Q: "On models of elementary elliptic geometry"

José Hdz. Stgo.While perusing p. 237 of the 3rd ed. of Marvin Greenberg's book on Euclidean and non-Euclidean geometries, I learned that it can actually be proven that "all possible models of hyperbolic geometry are isomorphic to one another, i.e., that the axioms for hyperbolic geometry are categorical". This ...

Q: Central limit theorem for irrational rotations

Nikita SidorovLet $\alpha$ be an algebraic integer of modulus 1, and $ R_\alpha z=\alpha z$. Is $$\lim_{n\to\infty}\frac{\log\sum_{k=1}^n \Re R_\alpha^k z}{\log n}=\frac12$$ for all $z\in S^1$?


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