# What does this symbol 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:$$\nVdash(n=k=0)$$

## Answers and Replies

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$A \nVdash B$).

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?

Staff Emeritus