## Chains, antichains, and complements in infinite partition lattices

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#### Standard

Chains, antichains, and complements in infinite partition lattices. / Avery, James Emil; Moyen, Jean-Yves; Ruzicka, Pavel; Simonsen, Jakob Grue.

I: Algebra Universalis, Bind 79, Nr. 37, 37, 2018.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Harvard

Avery, JE, Moyen, J-Y, Ruzicka, P & Simonsen, JG 2018, 'Chains, antichains, and complements in infinite partition lattices', Algebra Universalis, bind 79, nr. 37, 37. https://doi.org/10.1007/s00012-018-0514-z

#### APA

Avery, J. E., Moyen, J-Y., Ruzicka, P., & Simonsen, J. G. (2018). Chains, antichains, and complements in infinite partition lattices. Algebra Universalis, 79(37), [37]. https://doi.org/10.1007/s00012-018-0514-z

#### Vancouver

Avery JE, Moyen J-Y, Ruzicka P, Simonsen JG. Chains, antichains, and complements in infinite partition lattices. Algebra Universalis. 2018;79(37). 37. https://doi.org/10.1007/s00012-018-0514-z

#### Author

Avery, James Emil ; Moyen, Jean-Yves ; Ruzicka, Pavel ; Simonsen, Jakob Grue. / Chains, antichains, and complements in infinite partition lattices. I: Algebra Universalis. 2018 ; Bind 79, Nr. 37.

#### Bibtex

@article{54be2fafe45c45d49938dd1b575e502b,
title = "Chains, antichains, and complements in infinite partition lattices",
abstract = "We consider the partition lattice $\Pi_\kappa$ on any set of transfinite cardinality $\kappa$, and properties of $\Pi_\kappa$ whose analogues do not hold for finite cardinalities. Assuming the Axiom of Choice we prove: (I) the cardinality of any maximal well-ordered chain is between the cofinality $\mathrm{cf}(\kappa)$ and $\kappa$, and $\kappa$ always occurs as the cardinality of a maximal well-ordered chain; (II) there are maximal chains in $\Pi_\kappa$ of cardinality $> \kappa$; (III) if, for every ordinal $\delta$ with $|\delta|$ 2$.", keywords = "math.RA, 06B05 (Primary), 06C15 (Secondary)", author = "Avery, {James Emil} and Jean-Yves Moyen and Pavel Ruzicka and Simonsen, {Jakob Grue}", year = "2018", doi = "10.1007/s00012-018-0514-z", language = "English", volume = "79", journal = "Algebra Universalis", issn = "0002-5240", publisher = "Springer Basel AG", number = "37", } #### RIS TY - JOUR T1 - Chains, antichains, and complements in infinite partition lattices AU - Avery, James Emil AU - Moyen, Jean-Yves AU - Ruzicka, Pavel AU - Simonsen, Jakob Grue PY - 2018 Y1 - 2018 N2 - We consider the partition lattice$\Pi_\kappa$on any set of transfinite cardinality$\kappa$, and properties of$\Pi_\kappa$whose analogues do not hold for finite cardinalities. Assuming the Axiom of Choice we prove: (I) the cardinality of any maximal well-ordered chain is between the cofinality$\mathrm{cf}(\kappa)$and$\kappa$, and$\kappa$always occurs as the cardinality of a maximal well-ordered chain; (II) there are maximal chains in$\Pi_\kappa$of cardinality$> \kappa$; (III) if, for every ordinal$\delta$with$|\delta| $2$.

AB - We consider the partition lattice $\Pi_\kappa$ on any set of transfinite cardinality $\kappa$, and properties of $\Pi_\kappa$ whose analogues do not hold for finite cardinalities. Assuming the Axiom of Choice we prove: (I) the cardinality of any maximal well-ordered chain is between the cofinality $\mathrm{cf}(\kappa)$ and $\kappa$, and $\kappa$ always occurs as the cardinality of a maximal well-ordered chain; (II) there are maximal chains in $\Pi_\kappa$ of cardinality $> \kappa$; (III) if, for every ordinal $\delta$ with $|\delta|$ 2\$.

KW - math.RA

KW - 06B05 (Primary), 06C15 (Secondary)

U2 - 10.1007/s00012-018-0514-z

DO - 10.1007/s00012-018-0514-z

M3 - Journal article

VL - 79

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 37

M1 - 37

ER -

ID: 148648055