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@article{1390283, author = {Lieberman, Michael and Rosický, Jiří}, article_location = {Cambridge}, article_number = {3}, doi = {http://dx.doi.org/10.1017/jsl.2016.39}, keywords = {metric abstract elementary class; accessible category; complete metric space}, language = {eng}, issn = {0022-4812}, journal = {The Journal of Symbolic Logic}, title = {Metric abstract elementary classes as accessible categories}, volume = {82}, year = {2017} }
TY - JOUR ID - 1390283 AU - Lieberman, Michael - Rosický, Jiří PY - 2017 TI - Metric abstract elementary classes as accessible categories JF - The Journal of Symbolic Logic VL - 82 IS - 3 SP - 1022-1040 EP - 1022-1040 PB - CAMBRIDGE UNIV PRESS SN - 00224812 KW - metric abstract elementary class KW - accessible category KW - complete metric space N2 - We show that metric abstract elementary classes are coherent accessible categories with directed colimits, with concrete $\aleph_1$-directed colimits and concrete monomorphisms. More broadly, we define a notion of $\kappa$-concrete Abstract Elementary Class and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah's Presentation Theorem and a proof of the existence of an Ehrenfeucht-Mostowski functor in case the category is large. ER -
LIEBERMAN, Michael and Jiří ROSICKÝ. Metric abstract elementary classes as accessible categories. \textit{The Journal of Symbolic Logic}. Cambridge: CAMBRIDGE UNIV PRESS, 2017, vol.~82, No~3, p.~1022-1040. ISSN~0022-4812. Available from: https://dx.doi.org/10.1017/jsl.2016.39.
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