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THE FUNDAMENTAL THEOREM OF CENTRAL ELEMENT THEORY

Part of: Varieties Model theory

Published online by Cambridge University Press:  07 September 2020

MARIANA VANESA BADANO  and
DIEGO JOSE VAGGIONE
MARIANA VANESA BADANO
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA CÓRDOBA 5000, ARGENTINAE-mail: marianabadano@hotmail.comE-mail: dvaggione@gmail.com
DIEGO JOSE VAGGIONE
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA CÓRDOBA 5000, ARGENTINAE-mail: marianabadano@hotmail.comE-mail: dvaggione@gmail.com
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Abstract

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We give a short proof of the fundamental theorem of central element theory (see: Sanchez Terraf and Vaggione, Varieties with definable factor congruences, T.A.M.S. 361). The original proof is constructive and very involved and relies strongly on the fact that the class be a variety. Here we give a more direct nonconstructive proof which applies for the more general case of a first-order class which is both closed under the formation of direct products and direct factors.

Keywords

Boolean factor relationsdefinable factor relationscentral elementdirect productfactor congruence

MSC classification

Primary: 03C05: Equational classes, universal algebra
Secondary: 03C40: Interpolation, preservation, definability 08B25: Products, amalgamated products, and other kinds of limits and colimits
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 4 , December 2020 , pp. 1599 - 1606
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Copyright
© The Association for Symbolic Logic 2020

References

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