While reading Wikipedia I noticed the phrase "well-ordered language" in the following related to Gödel's completeness theorem:
The completeness theorem then says that for any first-order theory T with a well-orderable language, and any sentence s in the language of T
if s is a semantic consequence of T then s is a syntactic consequence of T.
Why did the authors need to specify a "well-ordered language" and what are the characteristics of a first order language that show that it is well-ordered?
Wikipedia contributors. (2019, June 10). Gödel's completeness theorem. In Wikipedia, The Free Encyclopedia. Retrieved 20:07, June 19, 2019, from https://en.wikipedia.org/w/index.php?title=G%C3%B6del%27s_completeness_theorem&oldid=901289398