Beth's Theorem is a fundamental result in set theory that establishes a hierarchy of infinite cardinal numbers. Specifically, it states that for any infinite cardinal number $$\kappa$$, the next larger cardinality is given by $$\beth_{n+1} = 2^{\beth_n}$$, where $$\beth_0$$ represents the cardinality of the natural numbers. This theorem has played an essential role in the development of model theory by influencing the understanding of sizes of infinite sets and their relationships.
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