On the axiomatisability of the dual of compact ordered spaces

Marco Abbadini; Luca Reggio

doi:10.1007/s10485-020-09604-y

On the axiomatisability of the dual of compact ordered spaces

Marco Abbadini
, Luca Reggio

Computer Science

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

Abstract

We provide a direct and elementary proof of the fact that the category of Nachbin’s compact ordered spaces is dually equivalent to an ℵ1-ary variety of algebras. Further, we show that ℵ1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.

Original language	English
Pages (from-to)	921-934
Journal	Applied Categorical Structures
Volume	28
Issue number	6
DOIs	https://doi.org/10.1007/s10485-020-09604-y
Publication status	Published - 2020

Keywords

Compact ordered spaces
Duality
Axiomatisability
Infinitary varieties

Access to Document

10.1007/s10485-020-09604-y

Cite this

@article{ffa42e6d6c5a4c689d986adf632d3f3b,

title = "On the axiomatisability of the dual of compact ordered spaces",

abstract = "We provide a direct and elementary proof of the fact that the category of Nachbin{\textquoteright}s compact ordered spaces is dually equivalent to an ℵ1-ary variety of algebras. Further, we show that ℵ1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.",

keywords = "Compact ordered spaces, Duality, Axiomatisability, Infinitary varieties",

author = "Marco Abbadini and Luca Reggio",

year = "2020",

doi = "10.1007/s10485-020-09604-y",

language = "English",

volume = "28",

pages = "921--934",

journal = "Applied Categorical Structures",

issn = "0927-2852",

publisher = "Springer",

number = "6",

}

TY - JOUR

T1 - On the axiomatisability of the dual of compact ordered spaces

AU - Abbadini, Marco

AU - Reggio, Luca

PY - 2020

Y1 - 2020

N2 - We provide a direct and elementary proof of the fact that the category of Nachbin’s compact ordered spaces is dually equivalent to an ℵ1-ary variety of algebras. Further, we show that ℵ1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.

AB - We provide a direct and elementary proof of the fact that the category of Nachbin’s compact ordered spaces is dually equivalent to an ℵ1-ary variety of algebras. Further, we show that ℵ1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.

KW - Compact ordered spaces

KW - Duality

KW - Axiomatisability

KW - Infinitary varieties

U2 - 10.1007/s10485-020-09604-y

DO - 10.1007/s10485-020-09604-y

M3 - Article

SN - 0927-2852

VL - 28

SP - 921

EP - 934

JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 6

ER -

On the axiomatisability of the dual of compact ordered spaces

Abstract

Keywords

Access to Document

Fingerprint

Cite this