# François G. Dorais

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bio website dorais.org location Hanover, NH age member for 3 years, 9 months seen Apr 12 at 15:34 profile views 531

I like math and a few other things...

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 Jul19 comment Uncountable dense subset whose complement is also uncountable and dense The only drawback is that you need some Axiom of Choice to get a basis for $\mathbb{R}$ over $\mathbb{Q}$... Jul19 comment Uncountable dense subset whose complement is also uncountable and dense It doesn't get much simpler than that! (Note that intersecting $(-\infty,0]$ with $\mathbb{R}$ is a bit redundant.) Jul19 answered Uncountable dense subset whose complement is also uncountable and dense Jul19 comment Silver indiscernibles and definable injections Apostolos has the right idea. Every Silver indiscernible is in fact inaccessible in $L$. There will be a constructible injection $\lambda \to \omega\times\alpha^{<\omega}$ if and only if $\lambda < \max((|\alpha|^+)^L,\omega_1^L)$. If $\alpha < i_\alpha$, then $i_\alpha$ is necessarily much larger than $\max((|\alpha|^+)^L,\omega_1^L)$. Jul19 comment Silver indiscernibles and constructibility No problem! It was a pleasure! Jul18 revised Silver indiscernibles and constructibility clarification; changed terminology to match the question Jul18 answered Silver indiscernibles and constructibility Jul18 revised How is Kleene's T predicate defined? added wikipedia links Jul18 answered How is Kleene's T predicate defined? Jul17 comment Estimation of factoring time of a $n$-digit number (current state of art) on a desktop @Gerry: I used the formula from Wikipedia, which says that $c = (64/9)^{1/3} + o(1)$. I did ignore the $o(1)$, but all I wanted is to illustrate the fast growth of this function. Jul17 comment Do there exist interesting binary relations satisfying reflexivity and symmetry, but not transitivity? These are well-known graphs with some very interesting open problems. But your post doesn't even mention why anyone should care about these graphs! Jul17 comment Estimation of factoring time of a $n$-digit number (current state of art) on a desktop @TaoLee: The number field sieve is only one step along the path of better and better factoring algorithms. It is conceivable that a clever new algoritm could factor RSA-2048 in a matter of days. Jul16 comment Estimation of factoring time of a $n$-digit number (current state of art) on a desktop @TauLee: You have the formula, just plug in $N$... For RSA-2048, I got $$152373858906444928985207904781622575.47$$ Jul14 answered Order type of uncountable set and order ordering Jul14 comment Is $\left\{ F\subseteq V | P(F) \right\} = \emptyset$ or $= \left\{ \emptyset \right\}$, if no $F$ satisfies $P$? If $\emptyset$ is in the set then $P(\emptyset)$ must be true. Jul11 comment A notion of topology for computability Hm. The first sentence is clearly false. Furthermore, computable topology (in the sense of Weihrauch) has nothing to do with the setup in the question. In computable topology, open sets are defined as usual but the functions between spaces are required to be computable with respect to a systems of notations for the spaces involved. Jul11 answered A notion of topology for computability Jul11 comment Algorithm to determine if a Diophantine Equation has an infinite number of solutions @Charles: Without $\exists$ and $\forall$ you don't even have bounded quantifiers, so it would take some serious effort to get most primitive recursive functions in this context. Jul11 comment Algorithm to determine if a Diophantine Equation has an infinite number of solutions @Charles: The paper does mention that the same result holds when adding exponentials provided Schanuel's Conjecture is true. However, even then, how do you define the corresponding logarithms without $\exists$ and $\forall$? Jul10 comment What is the intuition behind the “par” operator in linear logic? Do you have a proof of completeness for your game semantics? (If I remember correctly, the game semantics of Blass were not quite complete.)