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A271219 Number n of antichains of P(En) x En*, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En* that same set augmented with an (n+1)th element smaller than all others. 0
1, 5, 83, 28925, 7663696588 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
This sequence is, more interestingly, the number of logical consequence relations in (n+2)-valued logic, with no order between intermediate values (i.e., values other than 0 and 1), which are truth functional, identical to the standard logical consequence relation on bivalent propositions and value-monotonic (if the relation holds, it is preserved with stronger premises and/or weaker conclusions). See reference below.
In n-valued logic with all truth values strictly ordered, the number of logical consequence relations with the same properties is more standard, it corresponds to: A030662. It satisfies the same definition as this sequence except that En should now be understood as a well-ordered set of n elements.
LINKS
E. Chemla, P. Egré and B. Spector, Characterizing logical consequence in many-valued logics, Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016).
CROSSREFS
Sequence in context: A301811 A216146 A111834 * A359110 A187587 A006471
KEYWORD
nonn,more
AUTHOR
Emmanuel Chemla, Apr 02 2016
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)