A note on the fixed point for the polynomials of a Boolean algebra with an operator of endomorphism
type: Item
instance of: scholarly article
title: A note on the fixed point for the polynomials of a Boolean algebra with an operator of endomorphism
zbMATH Open document ID: 0938.06012
author: Giuliana Gnani
author: Giuliano Mazzanti
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-11-28T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108490
review text: The fixed-point problem for Boolean algebras with an endomorphism operator \(k\) is studied. It is proved that in every finite algebra of this kind there exist polynomials \(f(x)\) without fixed point. Some properties of these algebras are established.
Mathematics Subject Classification ID: 06E25
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 1319591
zbMATH Keywords: Boolean algebras with an endomorphism operator
zbMATH Keywords: fixed point
reviewed by: Manuel Abad
MaRDI profile type: Publication
cites work: The uniqueness of the fixed-point in every diagonalizable algebra. (The algebraization of the theories which express Theor. VIII.)
cites work: The lattice of modal logics: an algebraic investigation
cites work: Q4397069
cites work: Q3934450
cites work: Q5599137
cites work: An axiomatic approach to self-referential truth
cites work: A system of complete and consistent truth
cites work: Q3282928
cites work: Finite fixed point algebras are subdiagonalisable
cites work: Boolean Algebras with Operators. Part I
cites work: Boolean Algebras with Operators
cites work: Q4121962
cites work: A COMPLETENESS RESULT FOR FIXED‐POINT ALGEBRAS
cites work: Algebraization of quantifier logics, an introductory overview
cites work: An effective fixed-point theorem in intuitionistic diagonalizable algebras. (The algebraization of the theories which express Theor. IX.)
cites work: Fixed point algebras
cites work: Self-reference and modal logic
cites work: Provability interpretations of modal logic
cites work: Fixed points of endomorphisms
cites work: A lattice-theoretical fixpoint theorem and its applications
cites work: Q5678913
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description: scientific article; zbMATH DE number 1319591