Type-amalgamation properties and polygroupoids in stable theories

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids (which correspond to 2-ary polygroupoids in our terminology). The n-ary polygroupoids are definable in a mild expansion of the language (adding a predicate for a Morley sequence).

Original languageEnglish
Article number1550004
JournalJournal of Mathematical Logic
Volume15
Issue number1
DOIs
Publication statusPublished - 2015 Jun 10

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Amalgamation
Groupoids
Algebraic Structure
Predicate
High-dimensional
First-order
Generalise
Language

All Science Journal Classification (ASJC) codes

  • Logic

Cite this

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Type-amalgamation properties and polygroupoids in stable theories. / Goodrick, John; Kim, Byunghan; Kolesnikov, Alexei.

In: Journal of Mathematical Logic, Vol. 15, No. 1, 1550004, 10.06.2015.

Research output: Contribution to journalArticle

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