bio  website  math.cas.cz/~jerabek 

location  Prague  
age  38  
visits  member for  4 years, 6 months 
seen  14 hours ago  
stats  profile views  7,144 
I am a researcher at the Institute of Mathematics of the Czech Academy of Sciences. I work in the field of mathematical logic, specifically proof complexity (mainly subsystems of bounded arithmetic, but also propositional proof complexity) and nonclassical logics (admissible rules of modal, superintuitionistic, and other propositional logics).
15h

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Trivial zeroes of the Riemann Zeta function are simple
@Bazin: You should include your working definition of the zeta function in the question, as any answer will crucially depend on it. 
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awarded  nt.numbertheory 
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awarded  Nice Answer 
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Continued Fractions from Digit Streams
Well, what about it? 
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answered  Continued Fractions from Digit Streams 
Aug
25 
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Undecidable set of problems
What, if any, of the two occurrences of the word “decidable” in your post refer to algorithmic decidability of a set of finite strings, and what refer to unprovability and nonrefutability of a formula in a formal system? In the latter case, what is the system? 
Aug
25 
awarded  Good Answer 
Aug
24 
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What are key $\Sigma^0_2$ or $\Pi^0_3$ theorems?
What you are talking about are just unimportant syntactical details. What matters is that PCA can’t prove more $\Pi_2$ sentences than $I\Sigma_1$. (Specifically, one important point is that all relations in PCA are $\Sigma_1$definable, and in particular, being $\Sigma_1$ is preserved by taking transitive closure.) PRA can be considered in the orthodox sense just an equational theory, but it is quite often also defined as an equivalent regular FO theory, and then it is exactly the $\Pi_2$ fragment of $I\Sigma_1$. 
Aug
24 
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What are key $\Sigma^0_2$ or $\Pi^0_3$ theorems?
@LucasK.: The description of PCA in mathoverflow.net/q/208696 does not seem to include anything that would not formalize in $I\Sigma_1$, or for that matter in its $\Pi_2$ fragment, which is just PRA. Thus, PCA should be equivalent (or at least, included in) PRA, and much weaker than the $\Pi_2$ fragment of PA. 
Aug
23 
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What are key $\Sigma^0_2$ or $\Pi^0_3$ theorems?
Even better, the $\Pi^0_2$ fragment of PA is axiomatized by the uniform $\Sigma_1$ reflection schema for finite subtheries of PA (that is, for the theories $I\Sigma_n$) 
Aug
20 
answered  Has by wellfoundedness every nonempty class an $R$minimal element? Also if axiom REG is not assumed? 
Aug
20 
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bound on the size of a circuit
These are not researchlevel questions. For a more appropriate site, you can try cs.stackexchange.com . 
Aug
20 
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Has by wellfoundedness every nonempty class an $R$minimal element? Also if axiom REG is not assumed?
Now that I think about it, the model constructed in Theorem 11 of our paper arxiv.org/abs/1311.0814 should do the job: it satisfies ZFC^ with collection, and there is a class carrying a dense linear order (with no least element) whose every subset is wellordered. 
Aug
20 
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Has by wellfoundedness every nonempty class an $R$minimal element? Also if axiom REG is not assumed?
Let $X$ be a class. First, by a straightforward induction on $n$, prove for all $n\in\omega$ that $X$ is a finite set with $< n$ elements, or it contains an $n$element subset. Thus, assuming $X$ is not a finite set, we have $\forall n\in\omega\,\exists x\subseteq X\,x=n$. Applying collection, there is a set $z$ such that $\forall n\in\omega\,\exists x\in z\,(x\subseteq X\landx=n)$. Then $X\cap\bigcup z$ is an infinite subset of $X$. 
Aug
20 
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Has by wellfoundedness every nonempty class an $R$minimal element? Also if axiom REG is not assumed?
That every proper class has an infinite subset is implied by collection, so I take it you don't include the collection schema in the list of axioms of ZFC^? 
Aug
14 
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Deciding a quadratic diophantine equation
The criterion should read that $ab$ is a square modulo $c$, $ac$ a square modulo $b$, and $bc$ a square modulo $a$. The statement with Legendre/Jacobi symbols is not in general equivalent to this unless $a,b,c$ are primes. Already in the simplest case $a=b=1$, it’s not true that a squarefree $c$ is a sum of two rational squares iff it is $\equiv1\pmod4$. 
Jul
17 
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A question on integers relatively prime to their Euler totien function
@JeremyRouse: I read the condition as “$Y$ be a subset of $X$ containing all prime numbers, and possibly some other numbers”. 
Jul
14 
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Lattices without prime ideals
Ah, sorry: they are meetirreducible, but not prime. However, they are most definitely proper ideals, so they need to be dealt with in the answer in one way or another. 
Jul
14 
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Lattices without prime ideals
The principal ideals generated by any $\alpha\in\kappa$ are all prime. 
Jul
14 
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Propositional logic without negation
Your implications are a notational variant for monotone sequents, so you might want to look into the monotone sequent calculus. 