Xi, Xiaoyong; Li, Yongming Exponentials in a Cartesian closed category which contains all algebraic domains. (English) Zbl 1330.18004 Appl. Categ. Struct. 23, No. 5, 665-672 (2015). Summary: The exponential is studied in the Cartesian closed category of all algebraic domains and all mappings which preserve directed suprema and the way-below relation. A problem presented by Z. Yang [Inf. Sci. 168, No. 1–4, 1–7 (2004; Zbl 1081.18010)] is partially solved. MSC: 18B35 Preorders, orders, domains and lattices (viewed as categories) 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) 06B35 Continuous lattices and posets, applications 68Q55 Semantics in the theory of computing Keywords:Cartesian closed; algebraic domains; way-below relation; exponential Citations:Zbl 1081.18010 PDFBibTeX XMLCite \textit{X. Xi} and \textit{Y. Li}, Appl. Categ. Struct. 23, No. 5, 665--672 (2015; Zbl 1330.18004) Full Text: DOI References: [1] Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E (eds.) Handbook of Logic in Computer Science, vol. 3, pp 1-168. Clarendon Press (1994) · Zbl 0923.54027 [2] Berry, G.: Stable models of typed λ-calculi. Lect. Notes Comput. Sci. 62, 72-88 (1978) · doi:10.1007/3-540-08860-1_7 [3] Chen, Y., Wu, H.: Domain semantics of possibility computations. Inf. Sci. 178, 2661-2679 (2008) · Zbl 1185.68403 · doi:10.1016/j.ins.2008.01.016 [4] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous Lattices and Domains. Cambridge Press, Cambridge (2002) · Zbl 1088.06001 [5] Gunter, G.; Scott, DS; Van Leeuwen, J. (ed.), Semantic domains (1990), Amsterdam · Zbl 0900.68301 [6] Liu, N., Li, S.: Cartesian closed stable categories. Inform. Sci. 171, 173-187 (2006) · Zbl 1081.18009 · doi:10.1016/j.ins.2004.04.001 [7] Mislove, M.W.: Topology, domain theory and theoretical computer science. Topolology Appl. 89, 3-59 (1998) · Zbl 0923.54027 · doi:10.1016/S0166-8641(97)00222-8 [8] Plotkin, G.D.: A powerdomain construction. SIAM J.Comp. 5, 452-487 (1976) · Zbl 0355.68015 · doi:10.1137/0205035 [9] Smyth, M.B.: The largest Cartesian closed category of domains. Theor. Comput. Sci. 27, 109-119 (1983) · Zbl 0556.68017 · doi:10.1016/0304-3975(83)90095-6 [10] Yang, Z.: A Cartisan closed subcategory of CONT which contains all continuous Domains. Inf. Sci. 168, 1-7 (2004) · Zbl 1081.18010 · doi:10.1016/j.ins.2003.06.006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.