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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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For the symmetric group on an infinite set, is there a generating set of strictly smaller ca... [closed]
Let $S_{\kappa}$ denote the symmetric group on some set of cardinality $\kappa$. Does there exist a generating set $X \subset S_{\kappa}$ such that $|X| < |S_{\kappa}|$ ($\stackrel{?}{=} 2^{\kappa} …