first one seems ridiculously basic...the other one less so.(adsbygoogle = window.adsbygoogle || []).push({});

1. What is a set?

If I ask what is a vector, I can say it is something in a vector space. If I ask what is a group, I can see if it meets some simple criteria. The axioms of set theory say certain things are sets but is there something that could be turned into a definition for a set of the form, "x is a set iff.... ." For groups G, there is a way to finish that line "G is a group iff... ." Same for vectors. What about sets? (Please no circular definitions like a set is a collection. I'm after the actual definition from math.)

2. Is there a way to turn the question of axiom independence into any other type of problem? I don't know much about it but does forcing do that? There must be some way to recontextualize axioms as generators of a group or something with the rules of deductive calculus being the group operations, or something, isn't there? Not saying it would be a group but some algebraic structure...

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# Two foundation questions

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