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.
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Gabriele Gullà (2024) studied this question.
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