Sh:E59

• Shelah, S. General non-structure theory and constructing from linear orders; to appear in Beyond first order model theory II. Preprint. arXiv: 1011.3576
  Ch. III of The Non-Structure Theory" book [Sh:e]
• Abstract:
  The theme of the first two sections, is to prepare the framework of how from a “complicated” family of so called index models I \in K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders, trees with \kappa+1 levels (possibly with linear order on the set of successors of a member) and linearly ordered graphs; for this we formulate relevant complicatedness properties (called bigness).

  In the third section we show stronger results concerning linear orders. If for each linear order I of cardinality \lambda > \aleph_0 we can attach a model M_I \in K_\lambda in which the linear order can be embedded such that for enough cuts of I, their being omitted is reflected in M_I, then there are 2^\lambda non-isomorphic cases. We also do the work for some applications.

• Version 2022-10-31 (59p)

@unpublished{Sh:E59,
 author = {Shelah, Saharon},
 title = {{General non-structure theory and constructing from linear orders; to appear in Beyond first order model theory II}},
 note = {\href{https://arxiv.org/abs/1011.3576}{arXiv: 1011.3576} Ch. III of  The Non-Structure Theory" book [Sh:e]},
 arxiv_number = {1011.3576},
 refers_to_entry = {Ch. III of  The Non-Structure Theory" book [Sh:e]}
}