 algebra system as 1920's algebra accept scienc studi properti set defin system oper howev forti overwhelm major algebraist investig kind algebra structur these group ring lattic the gener theoret work deal arbitrari set arbitrari oper g birkhoff 1935 dure year a tarski publish paper formul basic principl theori set equip system relat such set call model in contrast algebra model theori abund apparatu mathemat logic the possibl make fruit logic studi univers algebra classic part algebra group theori discov author 1936 dure twenti-five year gradual clear theori univers algebra model theori intim despit differ natur problem and meaning speak singl theori algebra system deal set defin seri oper relat algebra system the formal apparatu theori languag so-call appli predic calculu thu theori consid border logic algebra 