Makowsky and Shelah introduce a logic $L^{\text {pos }}$ - The usual formation rules for $\neg, \wedge, \exists x, \forall x$ - if $\varphi\left(s_{+}\right)$ is a formula of $L^{\text {pos }}$ in which $s$ occurs positively, then $\exists s \varphi\left(s_{+}\right)$ is a formula of $L^{\text {pos }}$. - if $\varphi\left(s_{-}\right)$ is a formula in which $s$ occurs negatively then $\forall s \varphi\left(s_{-}\right)$ is a formula. The semantics is given by $\mathfrak{M} \vDash \exists s \varphi(s)$ if there is a countable set $s$ such that $\mathfrak{M} \vDash \varphi(s)$. # Relations - properly containing $L(Q)$ [[Generalized logics#Generalized quantifiers]] - properly contained in [[Stationary logic]]