Very many clones above the unary clone

Martin Goldstern; Gábor Sági; Saharon Shelah

doi:10.1007/s00012-013-0236-1

Very many clones above the unary clone

Martin Goldstern, Gábor Sági^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let c:= 2^א0. We give a family of pairwise incomparable clones on ℕ with 2^c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2^c clones all with the same n-ary fragment, and all containing the set of all unary operations.

Original language	English
Pages (from-to)	387-399
Number of pages	13
Journal	Algebra Universalis
Volume	69
Issue number	4
DOIs	https://doi.org/10.1007/s00012-013-0236-1
State	Published - Jun 2013

Keywords

05C65
clones
monoidal interval
nonstructure
Primary: 08A40
Secondary: 05C25

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10.1007/s00012-013-0236-1

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abstract = "Let c:= 2א0. We give a family of pairwise incomparable clones on ℕ with 2c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2c clones all with the same n-ary fragment, and all containing the set of all unary operations.",

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author = "Martin Goldstern and G{\'a}bor S{\'a}gi and Saharon Shelah",

year = "2013",

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AU - Sági, Gábor

AU - Shelah, Saharon

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AB - Let c:= 2א0. We give a family of pairwise incomparable clones on ℕ with 2c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2c clones all with the same n-ary fragment, and all containing the set of all unary operations.

KW - 05C65

KW - clones

KW - monoidal interval

KW - nonstructure

KW - Primary: 08A40

KW - Secondary: 05C25

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VL - 69

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EP - 399

JO - Algebra Universalis

JF - Algebra Universalis

IS - 4

ER -

Very many clones above the unary clone

Abstract

Keywords

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