Unions, intersections and negations are available in types as well and are by no means exclusive to sets. The distinguishing feature of a set vs type is that a value belongs to just one type while it can belong to several sets.
replyTypes do not inherently have any such restrictions. A value can belong to several types. In fact, if you posit types to have union, that necessarily follows.
replyI think they do, and as you mentioned you can explicitly remove such a restriction. Sets and types are once again two different kinds of objects in mathematical theory, and a set-theoretic type doesn’t seem to be based either on set theory or type theory.
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