Vtyjkyuk

Edit: I should point out that, I tried searching by myself, but without success. Every time I thought I got the terminology correct, I tried to use it, but, I didn't get relevant results..

I'm taking a logic course in my native language, and I'm having trouble finding the same terminology in english. So here are a few questions.

the first expression, can be assigned True or False, is it called an Atom in english too?

$$ p_i $$
what would an expression like this be called?
$$
p_i land (neg p_j)
$$

what is the term for z called?
$$
z ⊨alpha
$$
here's a question from my homework:

prove the K "isn't definable".
$$
K = Ass backslash z
$$

what I mean mean by "isn't definable", is that there isn't a set like,
$$
Sigma = alpha,beta,...,theta
$$
that:
$$
M(Sigma)=K
$$

I hope I explained myself good enough. And thanks for anyone that would help :)

1) Yes, $p_i$ is a propositional variable or atom (or atomic formula): in the context of proposiational logic it represent an "undecomposable" sentence.

2) $p_i ∧ (¬p_j)$ is a formula and specifically a conjunction.

3) In an expression like $Gamma vDash alpha$, meaning that formula $alpha$ is logical consequence of the set $Gamma$ of formulas, we may call the formulas in $Gamma$ premises or assumptions.

But we can have also : $v vDash alpha$, where $v$ is a valuation (also called truth assignment), i.e. an assignment of truth values to propositional variables.

A valuation can be uniquely extended to an assignment of truth values to all propositional formulas.

Thus, $v vDash alpha$ means that valuation $v$ satisfies formula $alpha$, i.e. that $v$ assigns to $alpha$ the value TRUE.

I assume that $text Ass$ is the set of all valuations.

Thus, the question about definability of $K = text Ass setminus z $ amounts to :

find a set $Sigma = p_i mid ldots $ of propositional variables, such that $K$ is the set of models of $Sigma$ (call it : $text Mod (Sigma)$), i.e. the set of valuations that assign to the formulas in $Sigma$ the value TRUE (i.e. $textMod(Sigma) = v mid v text is a valuation and v vDash sigma text for every sigma in Sigma $).