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Suppose you face a proof system portraying some notion or knowledge that you haven't encountered, or others haven't studied before. What would be your first attempts to examine the consistency of the system?

I'm aware of two methods for proving consistency:

  • model construction
  • proof-theoretic techniques (such as Gentzen's)

What go-to techniques can one try if one encounters a novel proof system, as first attempts?

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    $\begingroup$ I don't know of a single instance where an ordinal analysis of a theory was provided before a relative consistency proof (keep in mind that for interesting theories all we can hope for is a relative consistency proof, per Godel). I'd say that model construction really is the go-to technique, although of course it's so broad that it itself has many sub-techniques and tricks. $\endgroup$
    – Noah Schweber
    Commented Jan 28, 2021 at 21:21
  • $\begingroup$ Thanks! Any suggestions of sub-techniques of model construction? $\endgroup$
    – qk11
    Commented Jan 28, 2021 at 23:02

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