Abstract:The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that structure. With this phenomenon and its twin sibling "reflection", modern set theory has settled many mathematical statements left undecided by the conventionally accepted formalism of mathematics, ZFC. There is a broad research program investigating whether a notion of comp… Show more
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