I've become accustomed to referring to - - coherent logic, with connectives true, /\, false, \/, = and (exists); and - geometric logic that also admits infinitary \/. I think I got this sense of "geometric" from Mike Fourman, and then "coherent" is natural because coherent theories are classified by coherent toposes. But the published works vary considerably. In particular, where I have coherent geometric, Makkai and Reyes have finitary coherent coherent, Johnstone has finitary geometric generalized geometric MacLane and Moerdijk have geometric (not referred to). Is usage as chaotic as it appears? Steve Vickers. ==============================================================================
This is Michael Makkai replying to Steve Vickers' query on coherent vs geometric logic. Despite the variety you found in the literature, I think you are right about the standard usage. I certainly have used the terms in those senses now for a long time (despite what appears in Makkai/Reyes). I think Andy Pitts will agree with me; in fact I vaguely recall that I told myself at one point that I would observe Pitts' usage in this respect. ==============================================================================
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