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I do not know much about mathematical logic but my understanding is that once an axiomatic system has a model, it is consistent. If this is the case what should be the characteristics of the model?

More specifically, what makes Dedekind cuts a suitable model for real numbers, from which we can conclude the consistency of the axiomatic system of real numbers?

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    $\begingroup$ That depends on your axioms. Essentially, you just verify all of them. This is often done in the first few weeks of calculus courses. $\endgroup$
    – Asaf Karagila ♦
    Commented May 9, 2017 at 5:29
  • $\begingroup$ Thanks but why verification of axioms by cuts of rational numbers is sufficient? $\endgroup$
    – abk
    Commented May 9, 2017 at 6:34
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    $\begingroup$ How else do you plan on checking that something is a model of your axioms? $\endgroup$
    – Asaf Karagila ♦
    Commented May 9, 2017 at 6:47
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    $\begingroup$ You check to see if the axiom holds or not... $\endgroup$
    – Asaf Karagila ♦
    Commented May 9, 2017 at 8:38
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    $\begingroup$ Physical interpretation has absolutely no room in mathematics. At best it can be used as a guiding intuition, but even that is far fetched in mathematical logic and foundations of mathematics. $\endgroup$
    – Asaf Karagila ♦
    Commented May 10, 2017 at 5:40

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