TY - JOUR
T1 - On local and non-local properties
AU - Gaifman, Haim
PY - 1982/1/1
Y1 - 1982/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77956947365&partnerID=8YFLogxK
U2 - 10.1016/S0049-237X(08)71879-2
DO - 10.1016/S0049-237X(08)71879-2
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77956947365
SN - 0049-237X
VL - 107
SP - 105
EP - 135
JO - Studies in Logic and the Foundations of Mathematics
JF - Studies in Logic and the Foundations of Mathematics
IS - C
ER -