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Reference.org
Induction, bounding and least number principles
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<p>In <a href="/facts/First-order_arithmetic/DhhDnNug">first-order arithmetic</a>, the induction principles, bounding principles, and least number principles are three related families of first-order principles, which may or may not hold in <a href="/facts/Non-standard_model_of_arithmetic/e3EktWqv">nonstandard models of arithmetic</a>. These principles are often used in <a href="/facts/Reverse_mathematics/nHLm6JUQ">reverse mathematics</a> to calibrate the axiomatic strength of theorems. </p>