Generalized filter models

✍ Scribed by Ines Margaria; Maddalena Zacchi

• Book ID: 104326756
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 187 KB
• Volume: 238
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(99)00083-3

✦ Synopsis

In this paper, starting from ÿlters which are a natural generalization of intersection ÿlters (Barendregt et al., J. Symbolic Logic 48 (1983) 931-940), the existence of ÿlter models and ÿlter semimodels for the -calculus is investigated. The construction of ÿlters is based on a Z-semilattice of types in which the subsets having inÿmum are given by a collection Z, called subset system. The set of representable functions is characterized in the obtained domain. In the case where the properties of the subset system Z guarantee the existence of a ÿlter model, the proof of soundness and completeness of the associated natural Z-type assignment system is routine.