✦ LIBER ✦
A local normal form theorem for infinitary logic with unary quantifiers
✍ Scribed by H. Jerome Keisler; Wafik Boulos Lotfallah
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 152 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ω(Q u ) ω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht-Fraïssé type game similar to the one in [9]. A consequence is that every sentence of L∞ω(Q u ) ω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form (∃ ≥i y) ψ(y), where ψ(y) has counting quantifiers restricted to the (2 n-1 -1)-neighborhood of y.