3,303 reputation
1835
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 38
visits member for 3 years, 4 months
seen 40 mins ago

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.


Sep
26
awarded  Custodian
Sep
26
reviewed Reviewed What is the biggest number ever used in a mathematical proof?
Sep
26
comment Weak categoricity in first order logic
... The "subclass of what" would have to be defined with respect to some "universe". The question would be whether the definition works for any "universe", even much weaker ones than ZFC. However, if the "universe" doesn't allow to talk about "isomorphism", then we can't say that we have defined the "standard natural numbers" up to isomorphism. So whether the definition succeeds in defining the natural numbers up to isomorphism depends at least a bit on the underlying set theory.
Sep
26
comment Weak categoricity in first order logic
@tomasz Using the notation and conventions of Ebbinghaus et al., a set of formulas in the language $L^S$ for $S=\{ \boldsymbol{\sigma}, 0 \}$ would suffice. However, it's probably better to work with a set of sentences instead of a set of formula (free variables are a subtle issue), in which case a set of sentences in the language $L_0^S$ for $S=\{ \boldsymbol{\sigma}, 0, \omega \}$ would suffice. (The sentences would be such that the constant $\omega$ is either equal to the constant $0$, or else a non-standard number.) However, I wonder more about the other part...
Sep
25
answered Weak categoricity in first order logic
Sep
2
answered Using the discrete fourier transform to approximate the regular fourier transform
Aug
31
comment Fourier transform of an exponentially attenuated function
We have $f(t)=\hat{H}(t+i\beta t)$, correct? So what is $\mathcal{F}\{ \hat{H}(\alpha t) \}$, assuming we can use the formula for real $\alpha$ also for complex $\alpha$, if the function is sufficiently nice.
Aug
25
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@HenningMakholm The difference is that the meaning of "well-formed definition which can be recognized to succeed" is closely linked to the meaning of "definable subset of the natural number". But my initial question is exactly about the problems of this notion. So does your comment answers the question? Ignoring the self reference, your sentence seems to be interpretable as a definition of a "subset" based on an infinite set of "definable subsets". I guess this definition will succeed, if the infinite set is "recursively enumerable". However, I will have to think about it to be sure.
Aug
25
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@HenningMakholm Note that being a well formed definition is only a prerequisite for being a well formed definition which succeeds. The intention of the concept well formed definition is to allow using human languages for the definitions without having to worry (too much) about the inaccuracies (and other issues) of human languages. On the other hand, dealing with paradoxes caused by self reference and other issues related to the mathematical content of the well formed definition is delegated to the concept of "can be recognized to succeed to define..."
Aug
23
answered What is the advantage and disadvantage of Hilbert System?
Aug
21
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@boumol If I just have to specify a recursively enumerable set like the odd numbers or the prime numbers, I could copy the important parts from the specification of a suitable programming language like Haskell into the ODF document, and then write a function in that language which enumerates all elements of that set. The intention of my last edition was to give a more rigorous meaning to "recursively enumerable" in the context of the question. It's OK that "definable" also got narrowed down a bit on the way, but it basically still means "define it however you like, if it is clear enough".
Aug
21
revised Is the set of all definable subsets of the natural numbers recursively enumerable?
Tried to formalize the use of recursively enumerable in the question
Aug
20
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@boumol I will have to think about it. The question was intended to mean "is the set of all definable subsets of the natural numbers countable in the way I interpreted countable before I learned about axiomatic set theory, ordinals, and all the other subtleties". However, I guess the answer of Carl Mummert will remain valid, even if I succeed to formulate the question in a more rigorous way.
Aug
20
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@boumol Assuming you're still sure the methods with a finitistic formula works (I'm not sure what this means exactly), can you expand your comment into an answer?
Aug
20
comment Is the set of all definable subsets of the natural numbers recursively enumerable?
@boumol It's true that the "Turing machine" only accepts finite inputs, but what do you mean by "it only produces finite outputs"? One natural way to define a subset of the natural numbers by a Turing machine would be to take the set of input numbers for which the machine stops. It should be clear from the question that any unambiguous way to define a subset of the natural numbers is acceptable. Especially if $S_1$ and $S_2$ are definable, then $S_1 - S_2$ is also definable. However, this doesn't mean that it is also definable as the set of input numbers for which some Turing machine stops.
Aug
20
comment A question about convolution of two distributions
@ShanLinHuang Yes, this is the intention of the condition. By the way, did you notice that I didn't really indicate how to show $u*v \in \mathcal{S}'(\mathbb R)$?
Aug
20
asked Is the set of all definable subsets of the natural numbers recursively enumerable?
Aug
19
revised Riemann hypothesis and diophantine equation
All references and diophantine equations for this I have seen so far are of the sort "RH <=> no solution"
Aug
19
suggested suggested edit on Riemann hypothesis and diophantine equation
Aug
15
comment A question about convolution of two distributions
I added a translation into english. I just found the mentioned lecture notes online: math.unice.fr/~frou/ACdistributions.html The cited theorem is from section II.4. However, it won't evoke the same emotions and memories for somebody who hasn't met André Cérezo...