Kaveh
Reputation
2,808
Top tag
Next privilege 3,000 Rep.
 Apr 11 comment Non-constructive proofs of decidability? IIRC, there is a similar theorem for set theory and $\Sigma_3$-formulas. Feb 29 revised Is the Riemann Hypothesis equivalent to a $\Pi_1$ sentence? adding complete title of papers, improving formatting Feb 10 revised What is a sieve and why are sieves useful? added 2 characters in body Feb 4 accepted Mapping an arrow from the direct limit of a diagram to the family of arrows from the diagram Feb 4 comment Mapping an arrow from the direct limit of a diagram to the family of arrows from the diagram I was hoping that if there is a general name then I can search for its examples in other fields and choose something from among their names. ps: maybe it is better to view $a$ as coproduct of the family in place of its direct limit and ask for a name for the restrictions of a function $f$ from $a$ to each member of the family. Feb 4 comment Mapping an arrow from the direct limit of a diagram to the family of arrows from the diagram Thanks Andrej, but I am looking for a name that does not refer to the cone since it is kind of fixed and obvious in my case plus my target audience might not know what is a cone. To be more specific, I am looking for what I should call the process of turning a function over $\Sigma^*$ to a family of functions with one for each input size. (I used $\mathbb{R}$ in the question because I felt it would be more familier to others and hoping that there is something like this in geometry). Feb 4 asked Mapping an arrow from the direct limit of a diagram to the family of arrows from the diagram Dec 29 awarded Nice Answer Nov 16 revised Semantic reflection added 4 characters in body Nov 16 comment Semantic reflection @Joel, sorry, but I don't see which part is confusing. Maybe I should have used $Tr_{\Phi}$. $Tr$ is a first-order formula that in the standard model represents the truth of formulas in $\Phi$. I don't talk about any model other than the standard model anywhere. The last part of your comment is not correct. It might help to think $\Phi$ as a complexity class like $NC^1$. (I used Godel coding because it is more familiar but it is not a good one from complexity perspective.) Nov 16 comment Semantic reflection @Joel, of course, that is why it is restricted to work only for $\Phi$. I don't think there is a need to state that $\Phi \subseteq \Sigma^0_n$. I have a class of formulas $\Phi$ and first-order formula that defines the truth predicate for the formulas in $\Phi$. If you want an example, check here. I just want to check if there is a standard name for the property before using something like "semantic reflection" to refer to it. Nov 16 revised Semantic reflection added 7 characters in body Nov 16 comment Semantic reflection @Joel, it is not true that PA cannot prove anything about Tr. It can for restricted classes of formulas e.g. $\Phi = \Sigma^0_0$. Nov 16 revised Semantic reflection added 40 characters in body Nov 15 revised Semantic reflection added 159 characters in body Nov 15 revised Semantic reflection added 159 characters in body Nov 13 revised A question on the name of a property added 14 characters in body Nov 13 comment Complexity classes for BSS machines You may want to check algebraic complexity and arithmetic circuit literature though I don't know if this particular measure has been studied. Nov 13 revised Semantic reflection added 213 characters in body Nov 13 asked Semantic reflection