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Finality regained: A coalgebraic study of Scott-sets and multisets

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Abstract

 In this paper we study iterated circular multisets in a coalgebraic framework. We will produce two essentially different universes of such sets. The unisets of the first universe will be shown to be precisely the sets of the Scott universe. The unisets of the second universe will be precisely the sets of the AFA-universe. We will have a closer look into the connection of the iterated circular multisets and arbitrary trees. RID=""ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B45, 03E65, 03E70, 18A15, 18A22, 18B05, 68Q85 RID=""ID="" <E5>Key words or phrases:</E5> Multiset &ndash; Non-wellfounded set &ndash; Scott-universe &ndash; AFA &ndash; Coalgebra &ndash; Modal logic &ndash; Graded modalities

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Authors and Affiliations

  1. Udine University, Department of Mathematics and Computer Science Viale delle Scienze 206, 33100 Udine, Italy. e-mail: dagostin@dimi.uniud.it, , , , , , IT

    Giovanna D'Agostino

  2. Utrecht University, Department of Philosophy Heidelberglaan 8, 3584 CS Utrecht, The Netherlands. e-mail: Albert.Visser@phil.uu.nl, , , , , , NL

    Albert Visser

Authors
  1. Giovanna D'Agostino
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  2. Albert Visser
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Received: 15 March 2000 / Published online: 25 February 2002

RID=""

ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B45, 03E65, 03E70, 18A15, 18A22, 18B05, 68Q85

RID=""

ID="" <E5>Key words or phrases:</E5> Multiset &ndash; Non-wellfounded set &ndash; Scott-universe &ndash; AFA &ndash; Coalgebra &ndash; Modal logic &ndash; Graded modalities

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D'Agostino, G., Visser, A. Finality regained: A coalgebraic study of Scott-sets and multisets . Arch. Math. Logic 41 , 267 –298 (2002). https://doi.org/10.1007/s001530100110

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  • DOI: https://doi.org/10.1007/s001530100110

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