2019/07/04 by Caicedo, Xavier, Duenez, Eduardo, Iovino, Jose
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1907.02398
The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if T is a theorem about convergence, then the fact that T is valid implies automatically that its (stronger) uniform version is valid, provided that T can be stated in certain logical frameworks. In this paper we identify precisely the logical frameworks L for which UMP holds. More precisely, we prove that the UMP holds for L if and only if L is a compact logic. We also prove a topological version of this equivalence. We conclude by proving new characterizations of logical compactness that yield additional information about the UMP.