This appears to be the earliest example of a purported proof of relative consistency, by which a theory is shown to be consistent lest another theory — whose consistency is typically taken for granted — be inconsistent.
The patterns of relative consistency for residues in different secondary structure types is similar for the most consistent methods (Fig. 4) although it varies for other, less consistent, methods (not shown).
In the most direct method of proving this theorem, the logician is provided with very useful tools in model theory and in studies on relative consistency and independence in set theory.
Forpadydeplasterer's relative consistency makes him a more obviously reliable candidate for the John Smith's Melling Chase, but stepping up in distance could suit an old rival rather better in Kalahari King (3.10).
In many cases not even relative consistency proofs are feasible.
The relative consistency of AC with ZF follows.
Gödel's is a relative consistency proof, obtained by constructing a so-called "inner model" for ZF together with the CH.
Thus, a proof of consistency or of undecidability of a given sentence $\varphi$ is always a relative consistency proof.
Relative consistency of this theory with the usual set theory ZFC is established via familiar results of model theory.
This model satisfies in this way the Continuum Hypothesis, and gives a relative consistency proof of this axiom.
That such a reinterpretation strategy guarantees relative consistency can be seen via the following reasoning: If the set AX were inconsistent, then it would logically imply a contradiction.
