Archive for Mathematical Logic

, Volume 39, Issue 8, pp 581–598 | Cite as

A strictly finitary non-triviality proof for a paraconsistent system of set theory deductively equivalent to classical ZFC minus foundation

  • Arief Daynes

Abstract.

The paraconsistent system CPQ-ZFC/F is defined. It is shown using strong non-finitary methods that the theorems of CPQ-ZFC/F are exactly the theorems of classical ZFC minus foundation. The proof presented in the paper uses the assumption that a strongly inaccessible cardinal exists. It is then shown using strictly finitary methods that CPQ-ZFC/F is non-trivial. CPQ-ZFC/F thus provides a formulation of set theory that has the same deductive power as the corresponding classical system but is more reliable in that non-triviality is provable by strictly finitary methods. This result does not contradict Gödel's incompleteness theorem because the proof of the deductive equivalence of the paraconsistent and classical systemss use non-finitary methods.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Arief Daynes
    • 1
  1. 1.Department of Accounting and Management Science, University of Portsmouth, Portsmouth Business School, Locksway Road, Milton, Southsea, Hants. PO4 8JF, England. e-mail: daynesa@pbs.port.ac.ukGB

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