2022/04/25 by Piotr Borodulin–Nadzieja, Piotr Borodulin-Nadzieja, Borodulin-Nadzieja, Piotr +2 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #math.LO
paper · pdf · doi:10.48550/arxiv.2204.11694
arxiv created 2022/04/25 · openalex publication_date 2022/04/25 · arxiv updated 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a finitely additive probability measure μ on ω is a P-measure if it vanishes on points and for each decreasing sequence (En) of infinite subsets of ω there is E⊆ω such that E⊆^* En for each n∈ω and μ(E) = limn→∞μ(En). Thus, P-measures generalize in a natural way P-points and it is known that, similarly as in the case of P-points, their existence is independent of ZFC. In this paper we show that there is a P-measure in the model obtained by adding any number of random reals to a model of CH. As a corollary, we obtain that in the classical random model ω^* contains a nowhere dense ccc closed P-set.