HIGHER RANDOMNESS AND GENERICITY
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DOI: 10.1017/fms.2017.27
Abstract: We use concepts of continuous higher randomness, developed in Bienvenu et al. [‘Continuous higher randomness’, J. Math. Log. 17(1) (2017).], to investigate $\unicode[STIX]{x1D6F1}_{1}^{1}$ -randomness. We discuss lowness for $\unicode[STIX]{x1D6F1}_{1}^{1}$ -randomness, cupping with $\unicode[STIX]{x1D6F1}_{1}^{1}$ -random sequences,… read more here.
Keywords: stix x1d6f1; higher randomness; randomness; randomness genericity ... See more keywords
ON -UNFAVOURABLE SPACES
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DOI: 10.1017/s0004972720000192
Abstract: To study when a paratopological group becomes a topological group, Arhangel’skii et al. [‘Topological games and topologies on groups’, Math. Maced. 8 (2010), 1–19] introduced the class of $(\,\unicode[STIX]{x1D6FD},G_{\unicode[STIX]{x1D6F1}})$-unfavourable spaces. We show that every $\unicode[STIX]{x1D707}$-complete (or normal)… read more here.
Keywords: stix x1d6f1; stix; unicode stix; stix x1d6fd ... See more keywords