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A local normal form theorem for infinitary logic with unary quantifiers
Author(s) -
Jerome Keisler H.,
Boulos Lotfallah Wafik
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200410013
Subject(s) - unary operation , mathematics , quantifier (linguistics) , rank (graph theory) , discrete mathematics , type (biology) , sentence , combinatorics , artificial intelligence , computer science , ecology , biology
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 . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)