What does this symbol mean?

weetabixharry

I would like to know what this symbol means:[tex]\nVdash[/tex]Specifically, in the main result of [link] (Theorem 1, at the top of p.4), it has:[tex]\nVdash(n=k=0)[/tex]

voko

It is negation of [tex]\Vdash[/tex] and the latter means "entails".

weetabixharry

Yes, I saw the [itex]\Vdash[/itex] symbol listed as "entails" in Wikipedia's list of mathematical symbols. However, in that article, the explanation is "A [itex]\Vdash[/itex] B means the sentence A entails the sentence B, that is in every model in which A is true, B is also true."

I can't see how that applies to my example (which is not in the form[itex]A \nVdash B[/itex]).

Bacle2

How about : the cases described are excluded, i.e., the definition excludes the

cases n=k=0 ?

weetabixharry

This still does not seem to make sense in the given context. The relevant phrase in full is:[tex]\mathrm{where \ } R_{n,0,k}(x) \ := \ \nVdash(n=k=0), \ \ R_{n,j,0} \ := \ \nVdash(n=j) \mathrm{ \ \ and \ \ } R_{n,j,k} \ := \ 0 \ \mathrm{else}[/tex]

weetabixharry

I've spent a long time trying to reverse engineer the phrase. My best guess is that the whole phrase (see previous post) could translate into the following two statements:

[tex]R_{n,0,k}=\left\{
\begin{array}{c}
1, \\
0,
\end{array}
\begin{array}{l}
\text{if }n=k=0 \\
\text{otherwise}
\end{array}
\right. [/tex]
[tex]R_{n,j,0}=\left\{
\begin{array}{c}
1, \\
0,
\end{array}
\begin{array}{l}
\text{if }n=j \\
\text{otherwise}
\end{array}
\right.[/tex]
Even if this is correct, there are other bits of notation that I don't understand... but I suppose I should start a new thread, as this one seems pretty dead.

voko

Why don't you get in touch with the author of the article?

micromass

Good idea. It looks like a typo. So you should ask the author.

weetabixharry

Yeah, I've E-mailed the author... fingers crossed that I get a reply, I suppose.