Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43810
Title: On Final Coalgebras of Power-Set Functors and Saturated Trees
Authors: Adámek, Jiří 
Levy, Paul B. 
Milius, Stefan 
Moss, Lawrence S. 
Sousa, Lurdes 
Issue Date: 2014
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Abstract: 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 P_λ, where λ is an infinite regular cardinal, we prove that the construction needs precisely λ+ω steps. We also generalize Worrell’s result to M-labeled trees for a commutative monoid M, yielding a final coalgebra for the corresponding functor ℳ_f studied by H.-P. Gumm and T. Schröder. We describe the final chain of the power-set functor by introducing the concept of i-saturated tree for all ordinals i, and then prove that for i of cofinality ω, the i-th step in the final chain consists of all i-saturated, strongly extensional trees.
URI: http://hdl.handle.net/10316/43810
Other Identifiers: 10.1007/s10485-014-9372-9
DOI: 10.1007/s10485-014-9372-9
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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