Interpolation and amalgamation properties in varieties of equivalential algebras

Studia Logica ◽  
1986 ◽  
Vol 45 (1) ◽  
pp. 35-38 ◽  
Author(s):  
Małgorzata Porębska
Keyword(s):  
Equivalential Algebras

Free spectra of linear equivalential algebras

2005 ◽  
Vol 70 (4) ◽  
pp. 1341-1358 ◽  
Author(s):  
Katarzyna Slomczyńska
Keyword(s):  
Free Algebras ◽  
Finitely Generated ◽  
Dummett Logic ◽  
Finite Height ◽  
Free Spectra ◽  
Equivalential Algebras

AbstractWe construct the finitely generated free algebras and determine the free spectra of varieties of linear equivalential algebras and linear equivalential algebras of finite height corresponding, respectively, to the equivalential fragments of intermediate Gödel-Dummett logic and intermediate finite-valued logics of Gödel. Thus we compute the number of purely equivalential propositional formulas in these logics in n variables for an arbitrary n ∈ ℕ.

Equivalential algebras. Part I: Representation

1996 ◽  
Vol 35 (4) ◽  
pp. 524-547 ◽  
Author(s):  
K. SŁomczyńska
Keyword(s):  
Equivalential Algebras

FREGEAN VARIETIES

2009 ◽  
Vol 19 (05) ◽  
pp. 595-645 ◽  
Author(s):  
PAWEŁ IDZIAK ◽  
KATARZYNA SŁOMCZYŃSKA ◽  
ANDRZEJ WROŃSKI
Keyword(s):  
Congruence Lattice ◽  
Propositional Logic ◽  
Finite Algebra ◽  
Constant Term ◽  
Intuitionistic Propositional Logic ◽  
Con A ◽  
Kripke Frames ◽  
Equivalential Algebras ◽  
Equivalential Fragment

A class [Formula: see text] of algebras with a distinguished constant term 0 is called Fregean if congruences of algebras in [Formula: see text] are uniquely determined by their 0–cosets and ΘA (0,a) = ΘA (0,b) implies a = b for all [Formula: see text]. The structure of Fregean varieties is investigated. In particular it is shown that every congruence permutable Fregean variety consists of algebras that are expansions of equivalential algebras, i.e. algebras that form an algebraization of the purely equivalential fragment of the intuitionistic propositional logic. Moreover the clone of polynomials of any finite algebra A from a congruence permutable Fregean variety is uniquely determined by the congruence lattice of A together with the commutator of congruences. Actually we show that such an algebra A itself can be recovered (up to polynomial equivalence) from its congruence lattice expanded by the commutator, i.e. the structure ( Con (A); ∧, ∨, [·,·]). This leads to Fregean frames, a notion that generalizes Kripke frames for intuitionistic propositional logic.

scholarly journals Free equivalential algebras

2008 ◽  
Vol 155 (2) ◽  
pp. 86-96 ◽  
Author(s):  
Katarzyna Słomczyńska
Keyword(s):  
Equivalential Algebras

scholarly journals The commutator in equivalential algebras and Fregean varieties

2011 ◽  
Vol 65 (4) ◽  
pp. 331-340 ◽  
Author(s):  
Paweł M. Idziak ◽  
Katarzyna Słomczyńska ◽  
Andrzej Wroński
Keyword(s):  
Equivalential Algebras

Equivalential algebras. Part II: Independence

1997 ◽  
Vol 37 (4) ◽  
pp. 426-439 ◽  
Author(s):  
K. S?omczy?ska
Keyword(s):  
Equivalential Algebras

scholarly journals Equivalential algebras with conjunction on the regular elements

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sławomir Przybyło
Keyword(s):  
Representation Theorem ◽  
Free Algebras ◽  
Finitely Generated ◽  
Regular Elements ◽  
Definition Of ◽  
Equivalential Algebra ◽  
Free Spectra ◽  
Equivalential Algebras

Abstract We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.

scholarly journals Definability of principal congruences in equivalential algebras

1998 ◽  
Vol 74 (2) ◽  
pp. 225-238 ◽  
Author(s):  
PaweŁ Idziak ◽  
Andrzej Wroński
Keyword(s):  
Equivalential Algebras
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