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Filters and congruences in sectionally pseudocomplemented lattices and posets
Ivan Chajda1, Helmut Länger1,2
1Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.
Soft Computing
|November 1, 2021
Summary
This study defines congruences and filters in sectionally pseudocomplemented lattices and posets. It explores their algebraic properties and potential as semantics for intuitionistic logics.
Area of Science:
- Algebraic structures
- Lattice theory
- Order theory
Background:
- Introduced sectionally pseudocomplemented lattices and posets.
- Explored their role in algebraic constructions.
- Hypothesized their connection to intuitionistic logics.
Purpose of the Study:
- Define congruences and filters in these structures.
- Investigate relationships between congruences and filters.
- Describe properties of congruences in strongly sectionally pseudocomplemented posets.
Main Methods:
- Utilized ideal terms and closedness concepts (A. Ursini).
- Applied algebraic tools to lattices and posets.
- Adapted machinery for non-everywhere-defined ideal terms in posets.
Main Results:
- Established definitions for congruences and filters.
- Derived mutual relationships between these algebraic concepts.
- Characterized basic properties of congruences in strongly sectionally pseudocomplemented posets.
Conclusions:
- Sectionally pseudocomplemented structures offer potential algebraic semantics for intuitionistic logics.
- The developed methods for filters are applicable to both lattices and posets.
- The study extends algebraic analysis to strongly sectionally pseudocomplemented posets.
Keywords:
Closedness of a subsetCongruenceCongruence classCongruence permutabilityDeductive systemFilterIdeal termMaltsev termPartial termSectionally pseudocomplemented latticeSectionally pseudocomplemented posetWeak regularityMore Related Videos
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