NDLI: Weakly extendable partial clones on an infinite set

Content Provider	Springer Nature Link
Author	Romov, Boris A.
Copyright Year	2016
Abstract	We consider local partial clones defined on an uncountable set E having the form Polp( $${\mathfrak{R}}$$ ), where $${\mathfrak{R}}$$ is a set of relations on E. We investigate the notion of weak extendability of partial clones of the type Polp( $${\mathfrak{R}}$$ ) (in the case of E countable, this coincides with the notion of extendability previously introduced by the author in 1987) which allows us to expand to uncountable sets results on the characterization of Galois-closed sets of relations as well as model-theoretical properties of a relational structure $${\mathfrak{R}}$$ . We establish criteria for positive primitive elimination sets (sets of positive primitive formulas over $${\mathfrak{R}}$$ through which any positive primitive definable relation over $${\mathfrak{R}}$$ can be expressed without existential quantifiers) for finite $${\mathfrak{R}}$$ as well as for $${\mathfrak{R}}$$ having only finite number of positive primitive definable relations of any arity. Emphasizing the difference between countable and uncountable sets, we show that, unlike in the countable case, the characterization of Galois-closed sets InvPol( $${\mathfrak{R}}$$ ) (that is, all relations which are invariant under all operations from the clone Pol( $${\mathfrak{R}}$$ ) defined on an uncountable set) cannot be obtained via the application of finite positive primitive formulas together with infinite intersections and unions of updirected sets of relations from $${\mathfrak{R}}$$ .
Ending Page	242
Page Count	12
Starting Page	231
File Format	PDF
ISSN	00025240
e-ISSN	14208911
Journal	algebra universalis
Issue Number	2
Volume Number	75
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-01-13
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	weakly extendable partial clone Algebra positive primitive elimination set weak polyhomogeneity Partial algebras positive primitive structure Relational systems, laws of composition
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On polymorphism-homogeneous relational structures and their clones

Endolocality meets homomorphism-homogeneity: a new approach in the study of relational algebras

Primitive positive clones of groupoids

Minimal clones—a minicourse

A survey of clones on infinite sets

CSP for binary conservative relational structures

Composition of matrix products and categorical equivalence

Meet-irreducible submaximal clones determined by nontrivial equivalence relations

On clones generated by primitive-positive operations of Tarski's relation algebras

Weakly extendable partial clones on an infinite set

Similar Documents

On polymorphism-homogeneous relational structures and their clones

Endolocality meets homomorphism-homogeneity: a new approach in the study of relational algebras

Primitive positive clones of groupoids

Minimal clones—a minicourse

A survey of clones on infinite sets

CSP for binary conservative relational structures

Composition of matrix products and categorical equivalence

Meet-irreducible submaximal clones determined by nontrivial equivalence relations

On clones generated by primitive-positive operations of Tarski's relation algebras

Weakly extendable partial clones on an infinite set