In set theory, Scott's trick is a method for choosing sets of representatives for equivalence classes without using the axiom of choice, if the axiom of regularity is available (Forster 2003:182). It can be used to define representatives for ordinal numbers in Zermelo–Fraenkel set theory. The method is named after Dana Scott, who was the first to apply it.
Beyond the problem of defining set representatives for ordinal numbers, Scott's trick can be used to obtain representatives for cardinal numbers and when taking ultrapowers of proper classes in model theory.
Read more about Scott's Trick: Application To Cardinalities
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