4,171 research outputs found
New examples of small Polish structures
We answer some questions from a paper of Krupi\'nski by giving suitable
examples of small Polish structures. First, we present a class of small Polish
group structures without generic elements. Next, we construct a first example
of a small non-zero-dimensional Polish -group
On \omega-categorical, generically stable groups
We prove that each \omega-categorical, generically stable group is
solvable-by-finite.Comment: 11 page
Left-ordered inp-minimal groups
We prove that any left-ordered inp-minimal group is abelian, and we provide
an example of a non-abelian left-ordered group of dp-rank 2
Locally finite profinite rings
We investigate the structure of locally finite profinite rings. We classify
(Jacobson-) semisimple locally finite profinite rings as products of complete
matrix rings of bounded cardinality over finite fields, and we prove that the
Jacobson radical of any locally finite profinite ring is nil of finite
nilexponent. Our results apply to the context of small compact -rings, where
we also obtain a description of possible actions of on the underlying ring.Comment: 17 page
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