# Sh:933

- Laskowski, M. C., & Shelah, S. (2015).
*\mathbf P-NDOP and \mathbf P-decompositions of \aleph_\epsilon-saturated models of superstable theories*. Fund. Math.,**229**(1), 47–81. arXiv: 1206.6028 DOI: 10.4064/fm229-1-2 MR: 3312115 -
Abstract:

Assume a complete first order theory T is superstable. We generalize revise [Sh:401] in two respects, so do not depend on it. First issue we deal with a more general case. Let \mathbf P be a class of regular types in \mathfrak{C}, closed under automorphisms and under \pm. We generalize [Sh:401] to this context to \mathbf P^\pm-saturated M’s, assuming \mathbf P-NDOP which is weaker than NDOP. Second issue, in this content it is more delicate to find sufficient condition on two \mathbf P-decomposition trees to give non-isomorphic models. For this we investigate natural structures on the set of regular types mod \pm in M. Actually it suffices to deal with the case M is \aleph_\varepsilon-saturated \mathfrak{d}_\ell = \langle M^\ell_\eta,a_\eta:\eta \in I_\ell\rangle is a \mathbf P-decomposition of M for \ell=1,2 and \{p^{\mathfrak{d}_\ell}_\eta:\eta \in I_\ell\}/\pm = ({\mathcal P} \cap \mathbf S(M))/\pm and show the two trees are quite similar (or isomorphic). - published version (36p)

Bib entry

@article{Sh:933, author = {Laskowski, Michael Chris and Shelah, Saharon}, title = {{$\mathbf P$-NDOP and $\mathbf P$-decompositions of $\aleph_\epsilon$-saturated models of superstable theories}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {229}, number = {1}, year = {2015}, pages = {47--81}, issn = {0016-2736}, doi = {10.4064/fm229-1-2}, mrclass = {03C45 (03C50)}, mrnumber = {3312115}, mrreviewer = {G. Cherlin}, doi = {10.4064/fm229-1-2}, note = {\href{https://arxiv.org/abs/1206.6028}{arXiv: 1206.6028}}, arxiv_number = {1206.6028} }