On Feb 16, 2:13 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > Student of Math <omar.hosse...@gmail.com> writes: > > > Any ways, there is my short paper and the idea of it is so simple to > > understand. > > What paper is that? > > > I shwed that The set which its exsitence is asserted by axiom of > > infinity, and it has no elements with an infinite descending chain > > each a member of the next is of the form (1) (the equation (1) in my > > paper), but (1) is not first-order experssible. > > It is well known that if ZFC is consistent it has non-wellfounded > models, e.g. by simple appeal to compactness. It seems you attach some > obscure significance to this technicality. Why is that? > > -- > Aatu Koskensilta (aatu.koskensi...@uta.fi) > > "Wovon man nicht sprechen kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
You can not advise consistency of ZF by its models, as there is no proof of the claim that ZF has a model. As you must know a first-order theory is consistent if and onlu if it has a model. So you have assumed S be true, and then you discuss if S is true or false?!