Abstract
Throughout this paper L denotes a complete lattice. That is a set of elements a, b, c, ⋯ partly ordered by a relation «⊂» such that to every class (aν) of elements aν in L there exists a greatest lower bound \( \mathop{ \cup }\limits_{\nu } \) aν in L. Then also the least upper bound \( \mathop{ \cup }\limits_{\nu } \)aν exists in L and furthermore there is a greatest element e in L, namely the g. l. b. of the empty subclass of L, and there exists the smallest element 0 in L, the g. l. b. of all elements of L.
Received September, 1952.
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© 1990 Springer-Verlag New York Inc.
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Buchi, J.R. (1990). Representation of Complete Lattices by Sets. In: Mac Lane, S., Siefkes, D. (eds) The Collected Works of J. Richard Büchi. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8928-6_7
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DOI: https://doi.org/10.1007/978-1-4613-8928-6_7
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