Strong amalgamation, Beck–Chevalley for equivalence relations and interpolation in algebraic logic
✍ Scribed by Adriana Galli; Gonzalo E. Reyes; Marta Sagastume
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 307 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0165-0114
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✦ Synopsis
We extend Makkai's proof of strong amalgamation (push-outs of monos along arbitrary maps are monos) from the category of Heyting algebras to a class which includes the categories of symmetric bounded distributive lattices, symmetric Heyting algebras, Heyting modal S4-algebras, Heyting modal bi-S4-algebras, and L x ukasiewicz n-valued algebras. We also extend and improve Pitt's proof that strong amalgamation implies Beck-Chevalley for ÿlters of Heyting algebras to exact categories with certain push-outs. As a consequence, a form of the Interpolation Lemma for some non-classical calculi is proved.