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%I #20 Dec 20 2019 11:30:16
%S 2,3,10,120549
%N Order of the domain D_n (n >= 0) in the inverse limit domain D_infinity.
%C D_infinity is the limit of the sequence of domains D_n that constitute the minimal nontrivial solution to the requirements that D_0 be a continuous lattice containing at least two elements and that D_(n+1) be the space of functions from D_n to D_n.
%D J. G. Sanderson, The Lambda Calculus, Lattice Theory and Reflexive Domains, Mathematical Institute Lecture Notes, University of Oxford, 1973.
%D J. E. Stoy, Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory, MIT Press, Cambridge, MA, 1977, pp. 113-115.
%H Encyclopedia of Mathematics, <a href="https://www.encyclopediaofmath.org/index.php/Continuous_lattice">Continuous lattice</a>.
%H Martin Richards, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.7113">Backtracking algorithms in MCPL using bit patterns and recursion</a>, University of Cambridge, 1997; see pp. 48-50. [It contains a program for the calculation of a(3) = |D_3|.]
%H A. W. [Bill] Roscoe, <a href="http://www.cs.ox.ac.uk/publications/publication1021-abstract.html">Notes on domain theory</a>, 2007; see p. 131.
%H A. W. [Bill] Roscoe, <a href="https://www.semanticscholar.org/paper/Notes-on-Domain-Theory-Roscoe/8e158398ce6ff2b7c441c82f270218dfef1cc27b">Notes on domain theory</a>, 2007; see p. 131.
%H Dana S. Scott, <a href="https://users.fit.cvut.cz/~staryja2/MIMSI/scott-continuous-lattices.pdf">Continuous lattices</a>, Technical Monograph PRG-7, Oxford University Computing Laboratory, 1971.
%H Dana S. Scott, <a href="https://doi.org/10.1007/BFb0073967">Continuous Lattices</a>, pp. 97-136 in F. W. Lawvere (ed.), Toposes, Algebraic Geometry and Logic, Springer-Verlag, Berlin, 1972.
%K nonn,more
%O 0,1
%A _Jon Awbrey_, Aug 16 2005
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