Submission date: 3 May 2023

Abstract:

Sh:E59. To appear in Beyond first order model theory II.

The theme of the first two sections, is to prepare the framework of how from a “complicated” family of so called index models I ∈ K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders, trees with κ + 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 λ > ℵ_0 we can attach a model M_I ∈ K_λ 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^λ non-isomorphic cases. We also do the work for some applications.

Mathematics Subject Classification: Primary 03C55, Secondary 03E05, 03E75, 03G05

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Full text arXiv 2305.02003: pdf, ps.