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Convergence in topological groups and the Cohen reals
Alexander Shibakov
We show that it is consistent to have an uncountable sequential group of intermediate sequential order while no countable such groups exist. This is proved by adding Cohen re…
Stack and register complexity of radix conversions
Motoya Machida, Alexander Shibakov
We investigate the question of computational resources (such as stacks and counters) necessary to perform radix conversions. To this end it is shown that no PDA can compute the sig…
On large sequential groups
Alexander Shibakov
We construct, using , an example of a sequential group such that the only countable sequential subgroups of are closed and discrete, and the only quotients of…
On sequential analytic groups
Alexander Shibakov
We answer a question of S.~Todorčević and C.~Uzcátegui from \cite{TU1} by showing that the only possible sequential orders of sequential analytic groups are and . Other re…
No interesting sequential groups
Alexander Shibakov
We prove that it is consistent with ZFC that no sequential topological groups of intermediate sequential orders exist. This shows that the answer to a 1981 question of P.~Nyikos is…