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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?
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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
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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
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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
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Nov
15
revised Semantic reflection
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Nov
15
revised Semantic reflection
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Nov
13
revised A question on the name of a property
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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
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Nov
13
asked Semantic reflection