My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.

17h
revised Is there a general notion of semigroup action?
Tried to me more explicit about my problems with respect to "how to make it work"
17h
comment Is there a general notion of semigroup action?
@AndrejBauer "..., so I don't really understand what you'd like." I want to understand how to make it work, including inverse semigroups and groupoids. As a first step, I try to get "implicit" agreement that the definition of groupoid action (and semigroupoid action/category action) is fine and "obvious". The challenging part is to see how inverse semigroups can be taken care of appropriately in the definition of semigroup action. One potential solution could also be to declare that an "inverse semigroups action" need not be a special case of a "semigroup action".
18h
revised Is there a general notion of semigroup action?
stupid me: a semigroupoid is just a category
18h
asked Is there a general notion of semigroup action?
Aug
26
comment Can there ever be symbolic formalism (of importance) without intuitive heuristics?
You ask: "What's the problem? Why not just write down an answer like ..."? The problem is that it is unclear what you are asking. For example, Jean-Yves Girard intented linear logic based on reasonable modifications of the structural rules of sequence calculus. Then he started trying to make sense out of his newly discovered logic. Of course, he also showed that he can reproduce classical and intuitionistic logic by adding the "of course" and "why not" operators. But this is cheating a bit, because this is already an extension of the basic system.
Aug
26
comment Can there ever be symbolic formalism (of importance) without intuitive heuristics?
In that case, does "lambda calculus" or "combinatorial logic" satisfy your requirements?
Aug
26
comment Can there ever be symbolic formalism (of importance) without intuitive heuristics?
OK, then I have no idea what you mean by "intuitive heuristics"! Why do you mean that "arrows in category theory" are an "intuitive heuristics"? I can't believe that you are asking whether there can ever be an symbolic formalism which is so obscure that it is intuitively completely impenetrable.
Aug
26
comment Can there ever be symbolic formalism (of importance) without intuitive heuristics?
You mean that "arrows in category theory" are an "intuitive heuristics", because the collection of morphisms from A to B is not necessarily a set? But the arrows themselves are still something "explicit", even if their collection is ill defined. Is it this sort of ill defined collection (which is present in essentially every formal symbolism I'm aware of) that worries you?
Aug
26
awarded Quorum
Aug
24
answered What is the definition of a $\Pi_1$-sentence?
Aug
24
revised Which ontological commitments are embedded in a straightforward Turing machine model?
added 4 characters in body
Aug
24
answered What is your understanding of Infinity?
Aug
24
reviewed Reviewed What is your understanding of Infinity?
Aug
24
reviewed Leave Open What is your understanding of Infinity?
Aug
24
answered Which ontological commitments are embedded in a straightforward Turing machine model?
Aug
21
comment Which ontological commitments are embedded in a straightforward Turing machine model?
See scottaaronson.com/blog/?p=1948#comment-114954 for an explanation, why the ontological commitment from a Turing machine model is always smaller than the existence of the Church-Kleene ordinal.
Aug
20
asked What is the definition of a $\Pi_1$-sentence?
Aug
19
comment Why isn't conceptual analysis considered part of logic?
How are ordered structures related to logic? Boolean algebra certainly is an ordered structure, but characterizing negation in terms of the order is not obvious. This problem is even worse for other ordered structures like residuated lattices commonly considered to form a logic. And things like linear logic even call into question whether a logic is necessarily an ordered structure, or whether a commutative monoid might also be enough.
Aug
18
answered How much maths can we do in NF(U)?
Aug
15
reviewed Satisfactory Computer science for programmers
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