On Complexity of Complete First‐Order Theories
Glen R. Cooper · Mathematical logic quarterly · 1982
i n g a on C 4 -P" the class T of dtl complete theories T which provides a measure of property i n ' T then T i s n o t Q-minimum and i f T i s not a-minimum then T i s not n,-categorical.H e a l s o d e f i n e s the v e r s a t i l i t y prop-----------------------e r t y and s b s that i f some f o f ~l t ~l a q ( x , y ) of T admits t h e versa-.t i l i t y p r o p e r t y iit T t h e n T isa-iaaxirwrm.S h e M 11971) d e f i n e s the order, strict order and independenoe -p r o p e r t i e s and sbws that T is unstable i f f same formula cp(x,y) o f -1 -T admits t h e o r d e r p r o p e r t y i n T i f f some fol~nula Jl(x,wf of T admits the strict o r d e r o r independence property i n T .Furthermore -h e s h a s that i f solc f & a plx,g) of T admits t h e order property -i n T then soee formula $if z,w) of T a d m i t s t h e finite cover -property in T .Be also shows t k t if some formula tp(x,y) of T admits the finite cover, o r d e r , or independence property i n T then soere formula $fz,Gf of T adaits the f i n i t e cover, order, o r independeqce property (respectively) i n T .This r e g u l t makes it easier to decide whether any formla of T adetits' any one of ' t h e s e -formula g(x,y) of T admits the finite cover property in T .