Horváth, Miklós; Joó, István; Szalkai, István On “Banach’s principle”. (Hungarian. English, Russian summaries) Zbl 0753.03020 Mat. Lapok 34, No. 4, 253-300 (1987). Summary: M. Ajtai proved [Period. Math. Hung. 5, 343-352 (1974; Zbl 0307.02046)] that adding a Cohen-generic real to any model of ZFC, in the generic extension every linear operator between Banach spaces (all the spaces and the operators are definable by first-order formulae) is continuous.When the formulae above satisfy certain absoluteness conditions, we can derive absolute theorems (see, e.g., Theorems 2.4 and 2.6). We generalize this and Ajtai’s other theorems in Theorems 4.15 and 4.21. Further, we give applications: derive absolute theorems in analysis using mathematical logical methods (Theorems 3.21 and 4.19). We also give an elementary introduction into the theory of first-order logics, constructive set theory (Section 1) and Cohen’s forcing method (Section 4). MSC: 03E35 Consistency and independence results 03E75 Applications of set theory 47S30 Constructive operator theory 46B99 Normed linear spaces and Banach spaces; Banach lattices Keywords:Cohen forcing; continuity of operators; Cohen-generic real; linear operator between Banach spaces; constructive set theory Citations:Zbl 0307.02046 PDFBibTeX XMLCite \textit{M. Horváth} et al., Mat. Lapok 34, No. 4, 253--300 (1987; Zbl 0753.03020)