TY - JOUR

T1 - Many symmetrically indivisible structures

AU - Meir, Nadav

N1 - Publisher Copyright:
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - A structure M in a first-order language L is indivisible if for every colouring of its universe M in two colours, there is a monochromatic M′⊆M such that M′≅M. Additionally, we say that M is symmetrically indivisible if M′ can be chosen to be symmetrically embedded in M (that is, every automorphism of M′ can be extended to an automorphism of M). In the following paper we give a general method for constructing new symmetrically indivisible structures out of existing ones. Using this method, we construct 2ℵ0 many non-isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from : Let M be a symmetrically indivisible structure in a language L. Let L0⊆L. Is M{up harpoon right}L0 symmetrically indivisible?.

AB - A structure M in a first-order language L is indivisible if for every colouring of its universe M in two colours, there is a monochromatic M′⊆M such that M′≅M. Additionally, we say that M is symmetrically indivisible if M′ can be chosen to be symmetrically embedded in M (that is, every automorphism of M′ can be extended to an automorphism of M). In the following paper we give a general method for constructing new symmetrically indivisible structures out of existing ones. Using this method, we construct 2ℵ0 many non-isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from : Let M be a symmetrically indivisible structure in a language L. Let L0⊆L. Is M{up harpoon right}L0 symmetrically indivisible?.

UR - http://www.scopus.com/inward/record.url?scp=84939424211&partnerID=8YFLogxK

U2 - 10.1002/malq.201400091

DO - 10.1002/malq.201400091

M3 - Article

AN - SCOPUS:84939424211

SN - 0942-5616

VL - 61

SP - 341

EP - 346

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 4-5

ER -