Timeline for General theory of the reals in Solovay-like models
Current License: CC BY-SA 4.0
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| Feb 5, 2020 at 10:33 | comment | added | Asaf Karagila♦ | Thanks, Haim. This is the sort of question I'm asking here, yes. I'm kind of interested in some commonalities, though. Which I expect we can find in the least sharp cardinal. (The dullest cardinal? I don't know, there's a joke about blades here, figure it out, you're a smart guy.) | |
| Feb 5, 2020 at 6:19 | history | edited | Asaf Karagila♦ |
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| Feb 5, 2020 at 3:38 | comment | added | Haim | A natural problem would be to look at consequences of AD that don't hold in the inaccessible Solovay model, but might hold in a Solovay model starting from a stronger large cardinal hypothesis. One such example that might be relevant is the conjunction of projective uniformization, projective Lebesgue measurability and projective Baire property, which was conjectured to be equivalent to PD, but was shown by Steel to hold in an appropriate $V^{Col(\omega, \lambda)}$ under a weaker large cardinal hypothesis. This is discussed in "Projective uniformization revisited" by Hauser and Schindler. | |
| Feb 4, 2020 at 13:20 | history | asked | Asaf Karagila♦ | CC BY-SA 4.0 |