Talk:Consequence operator

message: Mathematically, a "consequence operator" is just a finitary closure operator. A proposal for merging this article into closure operator was discussed in Talk:Closure operator. I don't understand why it failed. Apparently philosophy(?) is involved, although the article gives the impression of being basically about pure mathematics. (It appears from the discussion that "consequence operators" were renamed several times in the field where they are actually used, but not to "finitary closure operator" or "algebraic closure operator", the two well-known standard terms.)
What I also do not understand is why the categorisation that I have found here looked like advertising. I have removed "Model theory" because I am working in model theory and happen to know that "algebraic closure operator" is a relatively well-known term there because it's standard in universal algebra, while "consequence" has a specific meaning related to formulas. I removed "Algebra" for similar reasons.
I am not sure that this article should be in both "Logic" and "Mathematical Logic", but I leave this to someone closer to philosophy. What was said in the discussion in Talk:Closure operator doesn't convince me this belongs into Theoretical physics, either. But I will leave this to the experts. --Hans Adler (talk) 11:18, 23 November 2007 (UTC)
thread_title:  Failed merger with [[closure operator]] and categorisation 

message: Closure operators are certainly notable. It has been argued that the term "consequence operator", which is a synonym, should have its own article because the contexts in which this term is used are different, and an attempt to merge the two articles failed. However, this does not mean that this article should cover topics that are clearly not notable and would never survive in the main article on closure operators.
As far as I can tell (search in Google Scholar and Mathematical Reviews) the only person who ever wrote about "nonstandard consequence operators" in the sense of this article (there is another sense that is used in computer science) is the inventor himself. According to MathSciNet, only one of the numerous publications of this author has been cited by anyone else: two citations of a paper on topology. Based on these findings it seems clear that this is not a notable concept at all.
I will therefore remove the two paragraphs on nonstandard consequence operators. This makes the numerous references to works on the unrelated subject of nonstandard analysis unnecesseary, and so I will remove them as well. These changes make this article considerably shorter; I am happy to discuss them with anyone who feels they may not be in order. --Hans Adler (talk) 18:58, 21 January 2008 (UTC)
replies: text: I tend to agree; I haven't seem much evidence that nonstandard consequence operators are studied even by a group of researchers. On the other hand, I could be convinced that we should cover nonstandard consequence operators if evidence was presented. The section on criticism of nonstandard models never quite fit in, and I also agree with removing that. — Carl (CBM · talk) 12:49, 22 January 2008 (UTC)
replies: text: Well yes, of course. If people suddenly start recognising Herrmann's work, or if somebody reinvents the concept and gets attention for it, then it becomes notable and we can include these things again. And I never said the idea isn't interesting. In fact, it's so interesting that I would have studied Herrmann's papers if they weren't so obfuscated. --Hans Adler (talk) 13:07, 22 January 2008 (UTC)
thread_title:  Nonstandard consequence operators