Talk:Elementary class

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[edit] 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)

[edit] 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)