General non-structure theory

This was supposed to be an appendix to the book Non-structure, and probably will be, if it materializes. It presents relevant material sometimes new, which used in works which were supposed to be part of that book. In https://www.w3.org/1998/Math/MathML”> § https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429263637/26bd4099-d326-4c28-a33f-7985ba070843/content/matha0_32.tif” xmlns:xlink=“https://www.w3.org/1999/xlink”/> 1 we deal with partition theorems on trees with https://www.w3.org/1998/Math/MathML”> ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429263637/26bd4099-d326-4c28-a33f-7985ba070843/content/matha0_33.tif” xmlns:xlink=“https://www.w3.org/1999/xlink”/> levels; it is self contained. In https://www.w3.org/1998/Math/MathML”> § https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429263637/26bd4099-d326-4c28-a33f-7985ba070843/content/matha0_34.tif” xmlns:xlink=“https://www.w3.org/1999/xlink”/> 2 we deal with linear orders which are countable union of scattered ones with unary predicated, it is self contained. In https://www.w3.org/1998/Math/MathML”> § https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429263637/26bd4099-d326-4c28-a33f-7985ba070843/content/matha0_35.tif” xmlns:xlink=“https://www.w3.org/1999/xlink”/> 3 we deal mainly with pcf theory but just quote. In https://www.w3.org/1998/Math/MathML”> § https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429263637/26bd4099-d326-4c28-a33f-7985ba070843/content/matha0_36.tif” xmlns:xlink=“https://www.w3.org/1999/xlink”/> 4, on normal ideals, we repeat [Sh:247]. This is used in [Sh:331].