Timeline for Does V=L imply transitive containment over, say, Z?
Current License: CC BY-SA 3.0
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| Jul 6, 2014 at 23:26 | comment | added | Joel David Hamkins | Corrado, my understanding is that Mathias has proved that Z and also Mac do not prove that every set has a transitive closure. That was very surprising, since everyone thinks of $V_{\omega+\omega}$ as a "typical" kind of model of Z, but Mathias's models are far weirder. The question here is whether V=L is sufficient to rule out those pathologies. Of course the expectation is that it is, but this probably depends on exactly how $V=L$ is formulated, since in these weak theories, there are issues. | |
| Jul 6, 2014 at 23:13 | comment | added | Emil Jeřábek | ZF^- proves the existence of transitive closures, and you are using this fact throughout the whole argument, starting with the “As Kunen has proved...”. So, I fail to see how this answers the question. | |
| Jul 6, 2014 at 23:09 | comment | added | Colin McLarty | Thank you. But I am asking when V is closed under transitive closure, not just when there is inner model with transitive closures. | |
| Jul 6, 2014 at 23:03 | review | First posts | |||
| Jul 6, 2014 at 23:05 | |||||
| Jul 6, 2014 at 22:46 | history | answered | Corrado | CC BY-SA 3.0 |