The short answer is no. Con(T) is a very weak assumption and it is asking a lot for it to have interesting mathematical consequences. A slightly less ambitious question is whether "ZFC + the consistency of some large cardinal axiom" has any interesting mathematical consequences. Here the work of Harvey Friedman is relevant, as I explained in this answer to a related MO question. I don't think Friedman's examples aren't are quite there yet but they're getting close.
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The short answer is no. Con(T) is a very weak assumption and it is asking a lot for it to have interesting mathematical consequences. A slightly less ambitious question is whether "ZFC + the consistency of some large cardinal axiom" has any interesting mathematical consequences. Here the work of Harvey Friedman is relevant, as I explained in this answer to a related MO question. I don't think Friedman's examples are aren't quite there yet but they're getting close. |
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The short answer is no. Con(T) is a very weak assumption and it is asking a lot for it to have interesting mathematical consequences. A slightly less ambitious question is whether "ZFC + the consistency of some large cardinal axiom" has any interesting mathematical consequences. Here the work of Harvey Friedman is relevant, as I explained in this answer to a related MO question. I don't think Friedman's examples are quite there yet but they're getting close. |
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