2015/11/19 by Ramsey, Nicholas
#03C45 #03C55 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1511.06453
We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property κcdt(T), κsct(T), and κinp(T) and the relations that obtain between them. From strong colorings, we construct theories T with κcdt(T) > κsct(T) + κinp(T). We show that these invariants have distinct structural consequences, by investigating the decay of saturation in ultrapowers of models of T, where T is some theory with κcdt(T), κsct(T), or κinp(T) large and bounded. This answers some questions of Shelah.