Many symmetrically indivisible structures
release_ssatjbookvfsrotga2sngffrl4
by
Nadav Meir
2019
Abstract
A structure M in a first-order language L is
indivisible if for every coloring of M in two colors, 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
2^ℵ_0 many non-isomorphic symmetrically indivisible countable
structures in given (elementary) classes and answer negatively the following
question asked by A. Hasson, M. Kojman and A. Onshuus in "On symmetric
indivisibility of countable structures" (Cont. Math. 558(1):453–466): Let
M be a symmetrically indivisible structure in a language
L. Let L_0 ⊆L. Is ML_0 symmetrically indivisible?
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