Type-amalgamation properties and polygroupoids in stable theories

John Goodrick; Byunghan Kim; Alexei Kolesnikov

doi:10.1142/S021906131550004X

Type-amalgamation properties and polygroupoids in stable theories

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Article number	1550004
Journal	Journal of Mathematical Logic
Volume	15
Issue number	1
DOIs	https://doi.org/10.1142/S021906131550004X
Publication status	Published - 2015 Jun 10

Bibliographical note

Funding Information:
The second author was supported by NRF of Korea grant 2011-0021916, and Sam-sung Science Technology Foundation under project number SSTF-BA1301-03. The third author was partially supported by NSF grant DMS-0901315. We thank the anonymous referee for pointing out some minor errors in the original draft and for many helpful suggestions concerning the notation and terminology.

Publisher Copyright:
© 2015 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

Logic

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10.1142/S021906131550004X

Cite this

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Type-amalgamation properties and polygroupoids in stable theories

Abstract

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