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.

Oct
16
reviewed Approve suggested edit on coordinate geometry high level problems
Oct
7
comment Has philosophy ever clarified mathematics?
@AsafKaragila Nice. Maybe Kant caused mischief to philosophy, but the mischief to mankind probably had another source: language! What en.wikipedia.org/wiki/Standard_German describes is called Hochdeutsch, and it was an intentional invention. It had a similar purpose like the "Euro" currency in current times. One of the intentions was to create "reality" (the one they wished for and knew they wouldn't get), and that's just what it did (create and destroy more "reality" than its inventors could ever imagine)...
Oct
7
answered Has philosophy ever clarified mathematics?
Oct
7
reviewed Close Prove e is a loop iff it is in no spanning trees of G
Oct
7
reviewed Approve suggested edit on infinitely many solutions to $\displaystyle x^n + y^n = z^{n+1}$
Oct
7
comment Are higher order logics substantially stronger than second order
In a certain sense, this answer is only true if the other axioms ensure that there are infinitely many objects/elements in the universe. And if the other axioms already ensure that we have the consistency strength of bounded Zermelo set theory or ZFC set theory, then just adding higher order variables and impredicative comprehension axioms (without using higher order variables in some of the other axioms) won't increase consistency strength any further.
Oct
6
revised Are higher order logics substantially stronger than second order
Oh, I forgot that I wanted to say something about the last word property
Oct
6
answered Are higher order logics substantially stronger than second order
Oct
6
comment How much can investigating three nested systems help interpreting probabilistic theories?
@AsphirDom You may be right about the old days. Schrödinger's article is from 1935, the two text from Everett which I read are from 1956 and 1957, Bohm's first development of decoherence dates back to 1952 (in his article A Suggested Interpretation of the Quantum Theory in Terms of "Hidden Variables", which I didn't read), and Zeh's article On the Interpretation of Measurement in Quantum Theory, which finally lead to the general acceptance of decoherence, is from 1970. But some of the text books I read are newer than 2010, and still introduce these concepts by investigating nested systems.
Oct
6
asked How much can investigating three nested systems help interpreting probabilistic theories?
Oct
5
comment Is there any justification for the existence of sets?
@NickR Being a quotient object is a property of the object itself. Any operation or relation defined for the object has to respect it, otherwise it is "undefined". An equivalence class on the other hand can arise from context, without any far reaching consequences. It arose in this answer, because many canonical order relations are only preorders, i.e. reflexive and transitive, but not antisymmetric. But being a well order requires antisymmetry, so it made sense to only talk about the equivalence classes generated by the order.
Oct
5
revised Is multiplication in mixed radix numeral systems complicated?
edited tags
Oct
4
asked Is multiplication in mixed radix numeral systems complicated?
Oct
4
reviewed Excellent Is the golden rule considered childish in philosophy?
Oct
3
comment Are there *a priori* truths for a self-learning artificial intelligence system?
@user128932 Note that the A.I. system (from the question) has "unquestionable" assumptions both in its program structure and in the database, which cannot be "disproved internally" by any experience, even if they were wrong. As the described A.I. system has no way to run a program it 'made' directly on its own hardware, it will have to use its output data channels and actors to execute this program. It will have to learn the results produced by this program through its input data channels and sensors, and hence its results won't be able to "disprove" the database of "unquestionable" truths.
Oct
3
comment Are there *a priori* truths for a self-learning artificial intelligence system?
@user128932 Gerhard Gentzen proved the consistency of PA. He wasn't able to disprove the "theory that consistency is unprovable" by this. Harvey Friedman currently works towards explicit computer search for inconsistencies in ZFC. Even if an inconsistency should be found, this doesn't necessarily mean that the "theory that ZFC is consistent" will be disproved by this. I'm not sure exactly why, but it probably has at least two independent reasons: (1) A scientist might know certain "unquestionable" truths. (2) Interpretation of results of a computer program is context dependent (=not absolute).
Sep
30
awarded Explainer
Sep
30
awarded Explainer
Sep
30
awarded Explainer
Sep
30
reviewed Approve suggested edit on Peirce-Frege-Wittgenstein-Habermas merge
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