Finite quasivarieties and self-referential conditions
โ Scribed by Alexei Vernitski
- Book ID
- 106538861
- Publisher
- Springer Netherlands
- Year
- 2004
- Tongue
- English
- Weight
- 217 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0039-3215
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract A quasivariety is said to be __implicative__ if it is generated by a class of algebras with equationallyโdefinable implication of equalities. Implicative finitelyโgenerated quasivarieties appear naturally within logic, for instance, as equivalent quasivarieties of Gentzenโstyle calculi
We define the notion of strictly finitely based varieties of groups and determine which finite groups are strictly finitely based. Then we use this result to prove the existence of "very nonfinitely based" finite algebras, thereby solving two open problems in the theory of quasivarieties.