Reversals and recursive counterexamples from countable mathematics are lifted to higher-order theorems about nets, yielding principles like BOOT from monotone convergence for nets.
Brown, Notions of closed subsets of a complete separable metric spa ce in weak subsystems of second-order arithmetic , Logic and computation (Pittsburgh, PA, 1987), Con- temp
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Lifting countable to uncountable mathematics
Reversals and recursive counterexamples from countable mathematics are lifted to higher-order theorems about nets, yielding principles like BOOT from monotone convergence for nets.