2 research outputs found
Was Sierpinski right? IV
We prove for any mu = mu^{< mu}< theta < lambda, lambda large enough (just
strongly inaccessible Mahlo) the consistency of 2^mu = lambda-> [theta]^2_3 and
even 2^mu = lambda-> [theta]^2_{sigma,2} for sigma < mu . The new point is that
possibly theta > mu^+
On the existence of universal models
Suppose that , and we are considering
a theory . We give a criterion on which is sufficient for the consistent
existence of universal models of of size for
models of of size , and is meaningful when
. In fact, we work more generally with abstract
elementary classes. The criterion for the consistent existence of universals
applies to various well known theories, such as triangle-free graphs and simple
theories.
Having in mind possible applications in analysis, we further observe that for
such , for any fixed regular with
, it is consistent that and there is no
normed vector space over {\Bbf Q} of size which is universal for
normed vector spaces over {\Bbf Q} of dimension under the notion
of embedding which specifies such that \norm{h(x)}/\norm{x}\in
(a,b) for all