scholarly journals Model completion of scaled lattices and co‐Heyting algebras of p ‐adic semi‐algebraic sets

2019 ◽  
Vol 65 (3) ◽  
pp. 305-331
Author(s):  
Luck Darnière
Keyword(s):  
Heyting Algebras ◽  
Algebraic Sets ◽  
Model Completion

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

Affine algebraic sets relative to an algebraic theory

1999 ◽  
Vol 65 (1-2) ◽  
pp. 54-76 ◽  
Author(s):  
Yves Diers
Keyword(s):  
Algebraic Theory ◽  
Algebraic Sets

Points near real algebraic sets

2014 ◽  
Vol 142 (12) ◽  
pp. 4127-4132
Author(s):  
W. M. Schmidt ◽  
U. Zannier
Keyword(s):  
Algebraic Sets

Splittings in varieties of logic

2021 ◽  
pp. 1-48
Author(s):  
Brian A. Davey ◽  
Tomasz Kowalski ◽  
Christopher J. Taylor
Keyword(s):  
Residuated Lattices ◽  
Heyting Algebras ◽  
General Lemma ◽  
Negative Results ◽  
Splitting Algebras

We study splittings or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the non-splitting lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splitting algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double [Formula: see text]-algebras the only splitting algebras are the two-element and three-element chains.

Forbidden structures in Heyting algebras with respect to sublattices

2017 ◽  
Vol 11 ◽  
pp. 211-224
Author(s):  
Manish Agalave ◽  
R. S. Shewale ◽  
Vilas Kharat
Keyword(s):  
Heyting Algebras
Sign in / Sign up

Export Citation Format

Share Document