TY - JOUR
AU - Mortimer, Michael
AB -  I n the normal run of logical affairs, every language contains infinitely many variables. SJmildwe consider a language with only finitely many variables, our ability to prove, an(1 our ability to express become severely restricted. Restrictions of the former kind hnvc bwn studied by HENKLX and MONK (see [2] and [ 3 ] ) .Our concern in this paper i* with restrictions o f the latter kind; specifically, the existence of “axioms of infinity” i. V . wntcnws with only infinite models. I t is easily seen that, allowing tjhree variables, ~ u c h sentence exists-e.g. the axiom for a strict linear ordering without last element. (t i K siic*Ji n sentence using only one variable, but with function symbols. We prove t h a t t hcw two sentences represent the best results possible - i.e. there is no consistent sentt w without function symbols and using two variables which has only infinite models. ~ This answers a question raised by W. HODGES. a corollary we have SCOTT’S As result ( ~ c . c . (41) that thc theory of a language wit,h two variables and no function symbols is dwidable. Our first result puts 
TI - On languages with two variables
JF - Mathematical Logic Quarterly
DO - 10.1002/malq.19750210118
DA - 1975-01-01
UR - https://www.deepdyve.com/lp/wiley/on-languages-with-two-variables-fEE70se6Pr
SP - 135
EP - 140
VL - 21
IS - 1
DP - DeepDyve
ER -