Timeline for A question regarding the Hahn-Banach theorem
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2015 at 13:06 | comment | added | godelian | It's clear that such a measure must take values within $0$ and $1$, but in order to even state countable additivity you would need $B$ to have countable joins and meets, which is not necessarily going to happen. Regarding $WKL_0$, you need to specify which base theory and which statement of Hahn-Banach theorem you are considering. $ZF$ is too strong since it proves Weak König's lemma, and the general formulation of Hahn-Banach theorem as in the above equivalence involves arbitrary vector spaces not necessarily definable in second order arithmetic. | |
| Jan 12, 2015 at 12:24 | comment | added | Thomas Benjamin | Does this real-valued measure extend to a probability measure on $B$? Also, what about the equivalence of Hahn-Banach to $WKL_0$ in reverse mathematics? | |
| Jan 9, 2015 at 16:33 | history | answered | godelian | CC BY-SA 3.0 |