# What does this symbol mean?

## Main Question or Discussion Point

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:$$\nVdash(n=k=0)$$

## Answers and Replies

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

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 ?

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:$$\mathrm{where \ } R_{n,0,k}(x) \ := \ \nVdash(n=k=0), \ \ R_{n,j,0} \ := \ \nVdash(n=j) \mathrm{ \ \ and \ \ } R_{n,j,k} \ := \ 0 \ \mathrm{else}$$

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.

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

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.

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.