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I seen in many texts for set theory that ZFC forms a foundation for most of math, e.g. analysis, topology, algebra, etc. Are they any fields of mathematics that cannot be built on ZFC?

Ben Grossmann
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BENG
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  • The body question asks what math can't be built on ZFC but the title says what math can't be built off of ZFC. Which is it?? – bof Sep 25 '20 at 03:05
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    @bof Welcome to English, where the primary interpretation of both phrases is essentially the same. – Mark S. Sep 25 '20 at 12:17
  • @MarkS. One phrase is standard English, the other is gibberish. Mathematicians have more reason than most people to care about using the correct preposition, e.g., into or onto. – bof Sep 25 '20 at 12:33
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    @bof https://english.stackexchange.com/questions/15081/ and https://english.stackexchange.com/questions/102057/ support the claim (which matches my native speaker intuition) that in colloquial American English, "off of" is used in this context by some with essentially the same meaning as "on". In other dialects of English or contexts, "off of" might not be used at all. – Mark S. Sep 25 '20 at 13:01

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