Countable infinitary logic
= Countable infinitary logic
{title2=$L_{\omega_1,\omega}$}
The logic $L_{\omega_1,\omega}$ extends <first-order logic> by countable <logical conjunctions> and <logical disjunctions>. Each formula has finitely many <free variables>, and quantifier strings are finite. In a countable <first-order language>, every countable structure has a <Scott sentence> in this logic that characterizes its <isomorphism> class among countable structures.