Activity for Julius H.
| Type | On... | Excerpt | Status | Date |
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| Edit | Post #290945 | Initial revision | — | 3 months ago |
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What is a “first-order substructural logic that has a cut-free sequent calculus”? Is a first order sub-structural logic a synonym for a fragment of first order logic? Ie just some restriction on syntactic allowances, so we know we have a theory whose sentences are a subset of the theory of FOL? I read that in sequent calculus, a cut rule is a rather trivial sounding rule that i... (more) |
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| Edit | Post #290943 | Initial revision | — | 3 months ago |
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What is the significance of the K-axiom in modal logic S5? In normal modal logic S5, the K axiom says $\square (p \rightarrow q) \rightarrow (\square p \rightarrow \square q)$. First of all, is this an abuse of notation? https://en.m.wikipedia.org/wiki/S5(modallogic) The middle implication arrow is meta-logical, isn’t it? It’s saying, “if statement 1 i... (more) |
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| Edit | Post #290942 | Initial revision | — | 3 months ago |
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What is a one-variable fragment of first-order logic? It is said the one variable fragment of first order logic is FOL restricted to sentences of one variable. Does this mean in the entirety of the language, there is only a single distinct variable, ie $x$? Ie, I can have formulae like “for all x (x implies x)”, and never mention some other variab... (more) |
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| Edit | Post #290864 | Initial revision | — | 3 months ago |
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What is a dual object? According to Wikipedia, - A dual object in a monoidal category is analogous to the idea of a dual vector space. - Infinite dimensional vector spaces are not dualizable. - An object is often dualizable when it has a finiteness or compactness property. - A category in which all objects have... (more) |
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| Edit | Post #290854 | Initial revision | — | 3 months ago |
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Explain derived categories to someone without a strong background in homological algebra Wikipedia has ample information about derived categories but it is too sophisticated for me to take in. The derived category D(A) of an abelian category A is a category D(A) together with a functor Q: Kom(A) -> D(A), where Kom(A) is the category of cochain complexes on A. For example, if A is t... (more) |
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| Edit | Post #290803 | Initial revision | — | 3 months ago |
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What are the Peano axioms? According to Wikipedia, > The nine Peano axioms contain three types of statements. The first axiom asserts the existence of at least one member of the set of natural numbers. The next four are general statements about equality; in modern treatments these are often not taken as part of the Peano ax... (more) |
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| Comment | Post #290765 |
He clarified the problem for me (more) |
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| Edit | Post #290760 | Initial revision | — | 3 months ago |
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Articles, please! I noticed Codidact has the BRILLIANT innovation of allowing you to post articles, something I had sometimes wanted over on Stack Exchange! But it appears math doesn’t have this. Why not? We should. (more) |
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| Edit | Post #290746 |
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| Edit | Post #290746 | Initial revision | — | 3 months ago |
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A: A program which could derive theorems given formation rules in any modal logic? The following answer comes from Jason Rute, all credit goes to him: Ok, I am going to bite. As the commentators have already said, I think you are proposing a much more ambitious and difficult program than you realize. If you could get this to work well, it could conceivably be a paper in Na... (more) |
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| Edit | Post #290745 | Initial revision | — | 3 months ago |
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A program which could derive theorems given formation rules in any modal logic? There are multiple modal logics which have different formation rules: Imagealttext Suppose someone asked the intuitive question, "If phi were a theorem in a modal logic M, what general, related conclusions might be drawn from that being so?" (See What is the modality of a statement that follows... (more) |
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| Comment | Post #290744 |
Possibly! Could you please elaborate on some of its mathematical properties, to help me understand if it matches what I was thinking of? Thank you! (more) |
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| Edit | Post #290742 |
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| Edit | Post #290742 |
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| Edit | Post #290742 | Initial revision | — | 3 months ago |
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Concrete examples of set theorists thinking independence proofs only determine provability rather than that a statement is neither true nor false? I’m curious to know more about this quote from a paper by Joel David Hamkins. > The pervasive independence phenomenon in set theory is described on this view as a distraction, a side discussion about provability rather than truth — about the weakness of our theories in finding the truth, rather th... (more) |
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| Edit | Post #290740 | Initial revision | — | 3 months ago |
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What are the “increasingly stable consequences of the large cardinal hierarchy”? I would like to understand the following quote, from a paper 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 regularit... (more) |
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| Edit | Post #290728 | Initial revision | — | 3 months ago |
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Cyclical or “loop” fractals? I want to ask an intuitively conceived question about “fractal loops”. However, I don’t know the mathematical definition of a fractal perfectly, off the top of my head. Because you can “zoom in” infinitely into fractals, I suppose the idea is there is some function specifying the data of the fract... (more) |
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| Comment | Post #290727 |
I love that. I hope we can bring that content over here to Codidact? New here, I don’t 100% know if there’s any sort of open license on the content there. But I’ll gladly summarize or repost it here. (more) |
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| Comment | Post #290727 |
> the Axiom of Infinity does assert the existence of a set, so this isn't an issue for ZFC.
I see. Perhaps I misremembered what I had read somewhere - that it is not FOL that implies the existence of “something”, but rather, the axiom of infinity. That’s very helpful. Thank you.
The axiom of in... (more) |
— | 3 months ago |
| Comment | Post #290727 |
Thanks a lot. I’d love to go through what you just said and perhaps have an extended conversation about this. That way, I could hopefully go back and revise and improve my post.
“*FOL is a specification language.*” Could you elaborate on the significance of this? In other words - a specification l... (more) |
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| Edit | Post #290727 | Initial revision | — | 3 months ago |
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Defining Bayes’s theorem from scratch in ZFC I have tons of interrelated questions which I would like resolved in order to help me answer this Philosophy SE question about Bayes’s theorem given a certain probability of 0. I’ll assume I am working in ZFC, which I have tons of questions about. In fact, I am still seeking even a basic underst... (more) |
— | 3 months ago |