Talk:Elementary class

Overlap with pseudoelementary classes

After putting some work into this article I realised that there is also an excellent article on pseudoelementary classes, from the point of view of universal algebra, which was started by Prof. Pratt. Unfortunately, this is an example of a general problem. Currently the common foundations of model theory and of universal algebra are covered unsystematically, with unnecessary duplications, and with many inconsistencies even within each of the two subjects. I would like to hear other people's opinions on this. --Hans Adler 14:55, 13 November 2007 (UTC)

I think merging this article with the pseudoelementary class article, and covering both algebra and logic, would be an improvement. — Carl (CBM · talk) 20:58, 13 November 2007 (UTC)

An equally good case could be made for merging pseudoelementary class with reduct. The notions of elementary class and reduct are orthogonal, and the several examples of pseudoelementary classes in pseudoelementary class arguably illustrate the concept of reduct better than they do the concept of elementary class. I would be inclined to leave things stand as they are. If no one has any more concrete proposal I'll remove the tags suggesting the merge at some point. --Vaughan Pratt (talk) 15:36, 18 August 2009 (UTC)

Question

In the section on "An elementary, basic pseudoelementary class that is not basic elementary" section.

What is Tau? is that meant to be capital-T from the example? I don't see where Tau is introduced or defined. Zero sharp (talk) 22:16, 30 December 2007 (UTC)

If K were basic elementary, then K were axiomatised by a theory T consisting of a single sentence. Towards a contradiction, we assume that this is the case, and that T={τ}, so τ is this sentence. This is what happens in the sentence "Otherwise the infinite σ-structures would be precisely those which satisfy a certain first-order sentence τ." I now see it's a bit terse. Can you rewrite it to make it clearer? Otherwise I will think about it. (Or is it just a typographic problem? With my fonts and settings the first τ looks like a very small capital T, and the second $\;\!\tau$ looks like a proper tau in TeX.) --Hans Adler (talk) 16:27, 1 January 2008 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Elementary class/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Merge with pseudoelementary class? --Hans Adler 14:59, 13 November 2007 (UTC)

Last edited at 14:59, 13 November 2007 (UTC). Substituted at 02:02, 5 May 2016 (UTC)