•  3
    The article considers the specifics of network effects of communication in functioning of mass consciousness in the period of information warfare. Conclusions are based on data of research project «Mass consciousness in the zone of military conflict in the Donbas». We found that the Internet, and in particular social media, as well as offline communication networks make a serious competition and sometimes outpace traditional media as a source of information in those parts of the Luhanska oblast,…Read more
  •  33
    Thin Ultrafilters
    with IV Protasov
    Notre Dame Journal of Formal Logic 53 (1): 79-88. 2012.
    A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open