Abstract
In this paper, we aim to establish a concrete representation, as a family of sets, for every algebraic L-domain. We generalize the notion of a topped algebraic intersection structure to a locally algebraic intersection structure. Just as topped algebraic intersection structures are concrete representations of algebraic lattices, locally algebraic intersection structures are concrete representations of algebraic L-domains. This result extends the classic Stone’s representation theorem for Boolean algebras to the case of algebraic L-domains. In addition, it will be seen that many well-known representations of algebraic L-domains can be analyzed with the framework of locally algebraic intersection structures.
This work is supposed by Shandong Provincial Natural Science Foundation(ZR2022MA022).
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Zou, J., Zhao, Y., Miao, C., Wang, L. (2022). A Set-Theoretic Representation of Algebraic L-domains. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_30
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