Definition talk:Ordered Set

Don't know if this would be instructive: A mention that this specifically does not include a preordered set.


 * No, because an ordered set is a priori a preordered set.


 * We can link to preordered set if you like, but your suggestion is like saying "a mention on Definition:Rational Number that this does not include an Definition:Integer. --prime mover (talk) 12:36, 7 March 2013 (UTC)

Classes again
The nice thing about "ordered structure" is that it doesn't have the word "set" in it. What do we call a relational structure whose relation is an ordering on a class? --Dfeuer (talk) 22:48, 21 March 2013 (UTC)


 * The disadvantage to "ordered structure" is that it usually means something other than "ordered set". "What do we call ... ordering on a class?" A stinking bodge that deserves to be flushed down the toilet.


 * But what we do is the hard work underpinning the basics of what L_F was talking about before we embark on the fun stuff. If you're really interested in working towards a solution to this question that you have jumped in the middle of, then rather than worrying about trivial issues like names of stuff, you'd be establishing how to set up a technique whereby multiple axiom schemata can be paralleled. --prime mover (talk) 23:10, 21 March 2013 (UTC)


 * For now I will be working on this stuff in my sandbox. I don't know how to deal with parallel systems. A rigid approach would be to put each axiomatization in its own namespace and only allow theorems about *sets* (not classes) in (Main), but that seems a bit draconian, especially considering that order theory and (I'm given to understand) category theory often deal in proper classes. Unrelatedly, I want to re-raise my request for a Physics (or perhaps Science) namespace. --Dfeuer (talk) 23:23, 21 March 2013 (UTC)


 * And if you think everything to do with class theory deserves to be flushed, I'm afraid for your sake that there seems to be very little chance of that. Classes have been a subject of mathematical study for decades. Of course, if you can prove that NBG (or even Morse-Kelley) theory is inconsistent, you could possibly be on your way to getting your wish (and the respect of mathematicians around the world). --Dfeuer (talk) 23:27, 21 March 2013 (UTC)

There's currently no analogous definition for classes, this proof references it and there isn't a page to link it to. I'd also like to extend this to be for classes so that well orders can be induced on proper classes by bijecting them with the class of ordinals via limitation of size, but I currently can't as there's no corresponding definition. --TheoLaLeo (talk) 01:40, 24 November 2021 (UTC)