Many symmetrically indivisible structures

作者：Meir Nadav^*

来源：Mathematical Logic Quarterly, 2015, 61(4-5): 341-346.

DOI：10.1002/malq.201400091

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' subset of M such that M' congruent to 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 2(N0) many non-isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from [6]: Let M be a symmetrically indivisible structure in a language L. Let L-0 subset of L.

• 出版日期2015-8