A synthetic overview on some known characterizations of Woodin cardinals

This brief survey comes from the slides of a seminar I gave to philosophy of mathematics students. I will present some different characterizations of Woodin cardinals, including the one obtained by Ernest Schimmerling in [6]. I will try to give to this paper the most self-contained possible structure, also by showing explicitly just the proofs usually leaved to the reader, and giving exact references for the others.