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We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies...
H be the Herbrand normal form ofA andA
H,D a Herbrand realization ofA
H. We show
There is an example of an (open) theory ℐ+ with function parameters such that for someA not containing function parameters[Figure not available: see fulltext.]
Similar for first order theories ℐ+...
We prove that the automorphism group ofP(ω)/fin remains simple if ℵ2 Cohen reals are added to a model of ZFC+CH.
We define a generalized notion of rank for stable theories without dense forking chains, and use it to derive that every type is domination-equivalent to a finite product of regular types. We apply this to show that in a small theory admitting finite coding, no realisation of a nonforking...
We show that form, n≧1 the existence of a∏
indescribable cardinal is equiconsistent with the failure of the combinatorial principle[Figure not available: see fulltext.] at a∏
indescribable cardinal κ together with the Generalized Continuum Hypothesis.
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