Invariant Types in Model Theory

Abstract

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Weakly binary expansions of dense meet-trees

“…We first recall briefly its definition and some of its basic properties for the reader's convenience, and otherwise refer to [Men20b]. See also [Men20a] for a more extensive treatment.…”

“…Acknowledgements A large part of this paper first appeared in the author's PhD thesis [Men20a], supervised by Dugald Macpherson and Vincenzo Mantova. The material and presentation has been greatly improved by their comments and suggestions, on [Men20a] and on drafts of this manuscript; in particular, Definition 4.1 was suggested by Mantova.…”

“…Acknowledgements A large part of this paper first appeared in the author's PhD thesis [Men20a], supervised by Dugald Macpherson and Vincenzo Mantova. The material and presentation has been greatly improved by their comments and suggestions, on [Men20a] and on drafts of this manuscript; in particular, Definition 4.1 was suggested by Mantova. I would like to thank Itay Kaplan for bringing to my attention cone-expansions of dense meet-trees, and Predrag Tanović for the fruitful discussions on the global Rudin-Keisler preorder, which inspired Example 3.3.…”

“…on its own, the atomic relations being the traces on Y of ∅-definable relations of U. It is easy to obtain a proof of the following fact; the reader may find one in [Men20a,Proposition 2.3.31].…”

The domination monoid in o-minimal theories

“…We recall how the domination monoid Inv(U) is defined, together with some of its basic properties. See [Men20b] or [Men20a] for a more thorough treatment.…”