On finitely based consequence operations
✍ Scribed by Andrzej Wroński
- Publisher
- Springer Netherlands
- Year
- 1976
- Tongue
- English
- Weight
- 312 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0039-3215
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The main theorem says that a consequence operator is an effective part o~ the consequence operator ~or the classical propositional calculus iff it is a consequence operator ~or a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
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.