The relative consistency of system RRC* and some of its extensions

We present a relative consistency proof for second order systemRRC* and for certain important extensions of this system. The proof proceeds as follows: we prove first the equiconsistency of the strongest of such extensions (viz., systemH RRC*+(/CP**)) with second order systemT^*. Now, N. Cocchiarella has shown thatT^* is relatively consistent to systemT*+Ext; clearly, it follows thatH RRC*+(/CP**) is relatively consistent toT*+E_xt. As an immediate consequence, the relative consistency ofRRC* and the other extensions also follows, being all of them subsystems ofH RRC*+(/CP**).I am grateful to the referee for some modifications suggested to an earlier draft of this paper.Presented byMelvin Fitting