jerboa had introduced his `` opera on themes mathematical and metamathematical '' with an unnecessarily lengthy lecture outlining gdel 's theorem of incompleteness : to every -consistent recursive class of formulae there correspond recursive class-signs r , such that neither v gen r nor neg ( v gen r ) belongs to flg ( ) ( where v is the free variable of r ) or all consistent axiomatic formulations of number theory include undecidable propositions .