Timeline for Existence of 'uniform transformations' of sequences of rationals (apres Friedman)
Current License: CC BY-SA 3.0
16 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Mar 17, 2012 at 3:29 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
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| Mar 17, 2012 at 2:14 | answer | added | Aaron Meyerowitz | timeline score: 1 | |
| Mar 17, 2012 at 0:11 | comment | added | David Roberts♦ | Yes, I rephrased it, because that is what he looks like he is doing, e.g. here: math.osu.edu/~friedman.8/pdf/Suppes90th030712.pdf on slide 10 and here: math.osu.edu/~friedman.8/pdf/MaxIncHarv030512.pdf slide 16. I couldn't figure out what he meant by "Z+up(x) results from adding 1 to all coordinates greater than all coordinates outside Z+" for months - not that I thought too hard about it - until I saw his examples. | |
| Mar 17, 2012 at 0:05 | comment | added | François G. Dorais | Thanks! Friedman's definition "Z+up(x) results from adding 1 to all coordinates greater than all coordinates outside Z+" doesn't seem to agree with yours. | |
| Mar 17, 2012 at 0:02 | history | edited | François G. Dorais | CC BY-SA 3.0 |
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| Mar 16, 2012 at 20:31 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
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| Mar 16, 2012 at 13:15 | comment | added | François G. Dorais | Could you add a link to Friedman's original definition? | |
| Mar 15, 2012 at 23:49 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
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| Mar 15, 2012 at 23:48 | comment | added | David Roberts♦ | Thanks, Aaron. I really have no idea what $(x,Tx)$ means, that it is concatenation was only a guess. I will inquire further. | |
| Mar 15, 2012 at 17:26 | comment | added | Aaron Meyerowitz | I'm not sure about the definitions. The definition of uniform transformation implies that $x \sim Tx.$ But for $T=\mathbb{Z}^+\!\!\uparrow$ and $x= 3/2 ,1$ we have $y=Tx=3/2,2$ so order equivalence fails: $x_1 \gt x_2$ but $y_1 \lt y_2.$ My understanding is that Harvey Friedman goes to great effort to make his examples as natural seeming as possible. | |
| Mar 15, 2012 at 10:43 | comment | added | David Roberts♦ | @Michael, If you can draw it and scan it, then email it to me, I can post it somewhere online (or you can yourself). | |
| Mar 15, 2012 at 10:04 | comment | added | Not Mike | MO needs some sort of collaborative drawing board, then the above would make much more sense. | |
| Mar 15, 2012 at 10:01 | comment | added | Not Mike | Finite trees maybe, let a sequence of integers consist of some sort of branch, and at non-integers you have a branching node. The branching node splits based on some coding, but the idea would be to have the tree above the branching node coded by the rest of the sequence occurring after the fraction. In this way based on whatever coding you pick for how to split the branching nodes, the uniform transformation extends the tree above the root, by leaving non-branching nodes (ie integers) alone, and possibly adding more splits at a branching node (non-integers) | |
| Mar 15, 2012 at 1:55 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
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| Mar 15, 2012 at 1:10 | history | asked | David Roberts♦ | CC BY-SA 3.0 |