Timeline for What logic can express this sentence?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2015 at 1:55 | comment | added | Noah Schweber | @ToddTrimble That's a very fair point. (Off the top of my head, one reason to care is in case you want this expression to be part of a larger one - e.g. if you want to say something like, "$\forall \overline{x}\exists \overline{y}([x_i>y_i]\wedge ...)$", at which point it's not enough to just express it as a collection of sentences. Of course, you're right that the OP should say this.) | |
| Dec 28, 2015 at 1:51 | comment | added | Todd Trimble | @NoahSchweber Well, it's likely you're right, but (1) OP has never said so, and ought to; (2) I wonder what the point would be for that (why does OP care, what's the motivation, etc.). | |
| Dec 28, 2015 at 1:38 | comment | added | Noah Schweber | @ToddTrimble True; however, I understood the OP as asking for a logic which could express this as a single sentence. | |
| Dec 17, 2015 at 20:52 | comment | added | Todd Trimble | You can have infinitely many axioms for a first-order theory. So a list of axioms like $x_0 > y_0$, $x_1 > y_1$, ... is perfectly acceptable. Of course the theory might not be finitely axiomatizable, but I don't see that requirement in your question. | |
| Dec 17, 2015 at 18:45 | answer | added | cody | timeline score: 1 | |
| Dec 17, 2015 at 8:14 | comment | added | none | Wouldn't you usually write $x(i)$ and $y(i)$ as functions rather than $x_1, x_2, \dots, y_1, y_2,\dots$ as infinite collections of variables? Then in your expression $x_k$ and $y_k$ would just be alternate notation for $x(k)$ and $y(k)$. | |
| Dec 17, 2015 at 4:40 | history | edited | Yoav Kallus | CC BY-SA 3.0 |
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| Dec 17, 2015 at 3:32 | answer | added | Noah Schweber | timeline score: 7 | |
| Dec 17, 2015 at 3:26 | review | First posts | |||
| Dec 17, 2015 at 3:34 | |||||
| Dec 17, 2015 at 3:24 | history | asked | user84230 | CC BY-SA 3.0 |