A note on da Costa-Doria "exotic formalizations"

Abstract

We analyze N. C. A. da Costa and F. A. Doria’s “exotic formalization” of the conjecture P = NP [3–7]. For any standard axiomatic PA extension T and any number-theoretic sentence φ, we let φ := φ ∨ ¬Con (T) and prove the following “exotic” inferences 1–3. 1. T + φ is consistent, if so is T, 2. T + φ is consistent, provided that T + φ is ω-consistent, 3. T… (More)
DOI: 10.1007/s00153-010-0203-x

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