Abstract We show that Katětov and Rudin–Blass orders on summable tall ideals coincide. We prove that Katětov order on summable tall ideals is Galois–Tukey equivalent to $(\omega ^\omega ,\le ^*)$ . It follows that Katětov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that ${l_\infty }$ is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.

This paper aims to study the protection of data privacy in news crowdfunding in the era of artificial intelligence. This paper respectively quotes the encryption algorithm of artificial intelligence data protection and the BP neural network prediction model to analyze the data privacy protection in news crowdfunding in the artificial intelligence era. Finally, this paper also combines the questionnaire survey method to understand the public’s awareness of privacy. The results of this paper show that artificial intelligence can promote personal data awareness and privacy, improve personal data and privacy measures and methods, and improve the effectiveness and level of privacy and privacy. In the analysis, the survey found that male college students only have 81.1% of the cognition of personal trait information, only 78.5% of network trace information, and only 78.3% of female college students’ cognition of personal credit.

Abstract We investigate the Tukey order in the class of $F_{\sigma }$ ideals of subsets of $\omega $ . We show that no nontrivial $F_{\sigma }$ ideal is Tukey below a $G_{\delta }$ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets.