clique principle – A query concerning the “math tea” dispute Answer

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clique principle – A query concerning the “math tea” dispute

Joel David Hamkins revealed a paper the place he analyzes the “math tea” dispute, particularly, the dispute that some actual numbers are undefinable. He constructed a countable mannequin of clique principle the place all units are definable with out parameters, and this apparently reveals the flaw with the maths tea dispute. However, I quiet cerebrate some actual numbers are undefinable. Here is why. Since we all know that, “in the real universe”, the actual numbers are uncountable, they can not reconcile inside a countable mannequin $$M$$, plane if $$M$$ thinks the clique of reals in that mannequin are internally uncountable. So, mainly, I cerebrate any countable mannequin of clique principle won’t ever have all the “real” actual numbers, and because of this I cerebrate some actual numbers are undefinable. I’d love some clarification of this, and need to breathe corrected if I misunderstand one thing.

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