On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness (Q1295420)

Using methods developed in previous papers, the author finds arithmetic equivalents of higher-order systems containing arithmetical comprehension, choice and (classically incorrect) general uniform boundedness. A typical result: \(\text{EA}^2+ \text{AC}^{0,0}-\text{qf}+ \Pi^0_1- \text{AC}^-\) is conservative over \(\text{EA}+ \Sigma^0_1- \text{IA}\) for \(\Pi^0_3\)-sentences, where EA is Kalmar-elementary arithmetic and \(\text{EA}^2\) is its second-order extension.