Timeline for When more is less in logic
Current License: CC BY-SA 4.0
2 events
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| Dec 14, 2022 at 8:14 | comment | added | Sam Sanders | I am not going to say that the Axiom of Choice is out (because it even plays a crucial/essential role in real analysis and regulated functions). I will say that I prefer "basic" examples, like the following special case of FTC: for regulated $f : [0, 1] → \mathbb{R}$ such that $ F (x) := λx. \int_0^x f (t)dt$ exists, there is $x_0 ∈ (0,1)$ where $F$ is differentiable with derivative $f(x_0)$. When adding the extra "Baire 1" condition, the latter theorem is provable in fairly weak system; not so without this condition. | |
| Dec 13, 2022 at 21:43 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |