An Introduction to the Scott Complexity of Countable Structures and a Survey of Recent Results

Abstract Every countable structure has a sentence of the infinitary logic $\mathcal {L}_{\omega _1 \omega }$ which characterizes that up to isomorphism among structures. Such is called Scott sentence, and can be thought as description structure. The least complexity for measurement describing We begin with an introduction area, short simple proofs where possible, followed by survey recent advances.