What does the symbol Vdash mean?

[weetabixharry]

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

 

[voko]

It is negation of $$\Vdash$$ and the latter means "entails".

 

[weetabixharry]

It is negation of $$\Vdash$$ and the latter means "entails".

Yes, I saw the $\Vdash$ symbol listed as "entails" in Wikipedia's list of mathematical symbols. However, in that article, the explanation is "A $\Vdash$ 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$A \nVdash B$).

 

[Bacle2]

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

cases n=k=0 ?

 

[weetabixharry]

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

cases n=k=0 ?

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

 

[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:

$$R_{n,0,k}=\left\{ \begin{array}{c} 1, \\ 0, \end{array} \begin{array}{l} \text{if }n=k=0 \\ \text{otherwise} \end{array} \right.$$
$$R_{n,j,0}=\left\{ \begin{array}{c} 1, \\ 0, \end{array} \begin{array}{l} \text{if }n=j \\ \text{otherwise} \end{array} \right.$$
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]

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

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

 

[weetabixharry]

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

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