A NOTE ON FRAGMENTS OF UNIFORM REFLECTION IN SECOND ORDER ARITHMETIC

EMANUELE FRITTAION
2022 Bulletin of Symbolic Logic  
We consider fragments of uniform reflection for formulas in the analytic hierarchy over theories of second order arithmetic. The main result is that for any second order arithmetic theory T0 extending RCA0 and axiomatizable by a Π 1 k+2 sentence, and for any n ≥ k + 1, , where T is T0 augmented with full induction, and TI Π 1 n (ε0) − denotes the schema of transfinite induction up to ε0 for Π 1 n formulas without set parameters.
doi:10.1017/bsl.2022.23 fatcat:ojlgdpuea5hzhlx7evl35o26lq