Timeline for First order consequence of a combinatorial principle
Current License: CC BY-SA 3.0
15 events
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| Dec 8, 2013 at 8:02 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| Dec 8, 2013 at 7:39 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| May 19, 2013 at 14:54 | vote | accept | Jing Zhang | ||
| May 18, 2013 at 10:22 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| May 17, 2013 at 17:23 | answer | added | François G. Dorais | timeline score: 6 | |
| May 17, 2013 at 11:35 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| May 17, 2013 at 1:47 | comment | added | Jing Zhang | Yeah the first property was what I was asking about. | |
| May 17, 2013 at 0:39 | comment | added | Wei Wang | Should the property be as follows: $\forall X \exists g \forall f \leq_T X(g \text{ dominates } f)$? $\exists g \forall X \forall f \leq_T X(g \text{ dominates } f)$ is impossible, as $g$ can not dominate $g+1$. | |
| May 16, 2013 at 17:36 | comment | added | Jing Zhang | Indeed. That was poorly phrased. I was thinking about the confinality in the ordinal (in order to define a dominating function if any). In this case, it is indeed bounding schemes that may be helpful. | |
| May 16, 2013 at 17:31 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| May 16, 2013 at 17:29 | comment | added | Noah Schweber | Any nonstandard universe will be ill-founded, so not any kind of ordinal at all. "Regularity" can sort of be made sense of, through Bounding schemes; is that in fact what you mean? | |
| May 16, 2013 at 17:12 | comment | added | Jing Zhang | @Jason: Sorry for its being poorly phrased. I am actually looking for some non-standard model in which RCA_0 and Domination principle hold. My guess of the universe being a regular cardinal is not a characterization for sure because one could easily produce a counter-example. To be exact, I would love some examples of non-standard models in which the principle holds. | |
| May 16, 2013 at 17:09 | history | edited | Jing Zhang | CC BY-SA 3.0 |
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| May 16, 2013 at 17:03 | comment | added | Jason Rute | To clarify, what is the question? Are you looking for a characterization of models in which the domination principle holds? Or examples of non-standard models where the domination principle holds? Or an answer to your hypothesis about the ordinal that the first-order theory is isomorphic to (is this meant to be a characterization?)? (I don't know the answer to any of these, but I want to make sure your question is clear to others who may know.) | |
| May 16, 2013 at 13:34 | history | asked | Jing Zhang | CC BY-SA 3.0 |