NDLI: Neat embeddings as adjoint situations

Content Provider	Springer Nature Link
Author	Sayed Ahmed, Tarek
Copyright Year	2013
Abstract	Looking at the operation of forming neat $$\alpha $$ -reducts as a functor, with $$\alpha $$ an infinite ordinal, we investigate when such a functor obtained by truncating $$\omega $$ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric algebras of infinite dimension, endowed with the merry go round identities, fails to have the amalgamation property answering a question of Németi’s. We also study two variants of the so-called cylindric polyadic algebras introduced by Ferenczi (all are reducts of polyadic equality algebras, that are also varieties). We show that one is more cylindric than polyadic, and that the other is more polyadic than cylindric. Our classification is determined by results on neat embeddings and amalgamation expressed from the point of view of category theory, thereby witnessing, and, indeed, further emphasizing, the dichotomy between the cylindric and polyadic paradigms. For example, the first class does not have the unique neat embedding property, fails to have the amalgamation property and the neat reduct functor does not have a right adjoint, while the second class has the unique neat emdedding property, the superamalgamation property and the neat reduct functor is strongly invertible. Other results, like first order definability of the class of neat reducts and the class of completely representable algebras, confirming our classification along these lines are presented.
Starting Page	2223
Ending Page	2259
Page Count	37
File Format	PDF
ISSN	00397857
Journal	Synthese
Volume Number	192
Issue Number	7
e-ISSN	15730964
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-09-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algebraic logic Cylindric algebras Polyadic algebras Neat embeddings Adjoint situations Amalgamation Philosophy of Science Epistemology Logic Philosophy of Language Metaphysics
Content Type	Text
Resource Type	Article
Subject	Philosophy Social Sciences

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

Some results about neat reducts

On amalgamation of reducts of polyadic algebras

Probabilities defined on standard and non-standard cylindric set algebras

Amalgamation, interpolation and epimorphisms in algebraic logic

Representations of polyadic-like equality algebras

Finitary Polyadic Algebras from Cylindric Algebras

A construction of cylindric and polyadic algebras from atomic relation algebras

On Amalgamation in Algebras of Logic

Neat embeddings as adjoint situations

Neat embeddings as adjoint situations

Similar Documents

Some results about neat reducts

On amalgamation of reducts of polyadic algebras

Probabilities defined on standard and non-standard cylindric set algebras

Amalgamation, interpolation and epimorphisms in algebraic logic

Representations of polyadic-like equality algebras

Finitary Polyadic Algebras from Cylindric Algebras

A construction of cylindric and polyadic algebras from atomic relation algebras

On Amalgamation in Algebras of Logic

Neat embeddings as adjoint situations

Neat embeddings as adjoint situations