Abstract
M. Richter has proved that whenever a classK of ∑-structures has a finitary first-order axiomatization then the inclusionK ↪Str ∑ preserves all existing directed colimits (see [7]). We will generalize this result to classes of ∑-structures having an infinitary first-order axiomatization in a larger signature ∑′. We will also show that, as categories, these classes have a natural characterization.
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In honour of Dieter Pumplün on the occassion of his 60th birthday
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Rosický, J. More on directed colimits of models. Appl Categor Struct 2, 71–76 (1994). https://doi.org/10.1007/BF00878503
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DOI: https://doi.org/10.1007/BF00878503