No interesting sequential groups

Alexander Shibakov

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arXiv · 1604.08868

No interesting sequential groups

Alexander Shibakov

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Abstract

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 independent of the standard axioms of set theory. The model constructed also provides consistent answers to several questions of D.~Shakhmatov, S.~Todor\v{c}evi\'c and Uzc\'ategui. In particular, we show that it is consistent with ZFC that every countably compact sequential group is Fr\'echet-Urysohn.

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Alexander Shibakov. 2016-04-29. No interesting sequential groups. https://arxiv.org/abs/1604.08868

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