Abstract
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 *λ . Now, N. Cocchiarella has shown thatT *λ 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**).
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References
N. B. Cocchiarella,Frege's double correlation thesis and Quine's set theories NF and ML Journal of Philosophical Logic 14 (1985), pp. 1–39.
N. B. Cocchiarella,Logical Investigations of Predication Theory and the Problem of Universals Bibliopolis Press, Naples 1986.
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M. A. Freund, Ph.D. dissertation, Indiana University at Bloomington, 1989.
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I am grateful to the referee for some modifications suggested to an earlier draft of this paper.
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Freund, M.A. The relative consistency of system RRC* and some of its extensions. Stud Logica 53, 351–360 (1994). https://doi.org/10.1007/BF01057932
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DOI: https://doi.org/10.1007/BF01057932