On local and non-local properties

Haim Gaifman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

188 Scopus citations

Abstract

This chapter presents a method that is an analysis of first-order formulas in terms of local properties. A natural simple metric is used in model and the concept of a k-local formula is defined, where k is any natural number. The main theorem asserts that every first-order sentence, ϕ, is logically equivalent to a Boolean combination of sentences that assert, each, something of the following form: There exist “s” disjoint r-neighborhoods, each satisfying the r-local formula Ψ. If ϕ is a formula, one has to add to the combination r-local formulas in the free variables of ϕ. The theorem is proved by quantifier elimination.

Original languageEnglish
Pages (from-to)105-135
Number of pages31
JournalStudies in Logic and the Foundations of Mathematics
Volume107
Issue numberC
DOIs
StatePublished - 1 Jan 1982

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