A preservation theorem for equality-free Horn sentences (Q2734543)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A preservation theorem for equality-free Horn sentences |
scientific article; zbMATH DE number 1634472
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A preservation theorem for equality-free Horn sentences |
scientific article; zbMATH DE number 1634472 |
Statements
16 August 2001
0 references
Horn logic
0 references
preservation theorem
0 references
reduced products
0 references
Horn sentence
0 references
A preservation theorem for equality-free Horn sentences (English)
0 references
The author proves the following preservation theorem: a sentence is equivalent to a sentence of the Horn fragment of first-order logic without equality iff it is preserved under strict homomorphic images, strict homomorphic counter-images, and reduced products. Keisler (using the continuum hypothesis) and Galvin (without this hypothesis) proved that a sentence is equivalent to a Horn sentence in first-order logic iff it is preserved under reduced products. The present proof follows the main lines of the proof by Keisler and Galvin.
0 references
