On Final Coalgebras of Power-Set Functors and Saturated Trees
نویسندگان
چکیده
منابع مشابه
On Final Coalgebras of Power-Set Functors and Saturated Trees - To George Janelidze on the Occasion of His Sixtieth Birthday
The final coalgebra for the finite power-set functor was described by Worrell who also proved that the final chain converges in ω + ω steps. We describe the step ω as the set of saturated trees, a concept equivalent to the modally saturated trees introduced by K. Fine in the 1970s in his study of modal logic. And for the bounded power-set functors Pλ, where λ is an infinite regular cardinal, we...
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We combine ideas coming from several fields, including modal logic, coalgebra, and set theory. Modally saturated trees were introduced by K. Fine in 1975. We give a new purely combinatorial formulation of modally saturated trees, and we prove that they form the limit of the final ωopchain of the finite power-set functor Pf . From that, we derive an alternative proof of J. Worrell’s description ...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2014
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-014-9372-9