DescriptionInduction, bounding, least number principles.png
English: A schematic diagram of the induction, bounding, and least number principles of first-order arithmetic. Vertical positioning determines logical implication over PA⁻ + IΣ₀ (i.e. strictly higher axioms are strictly stronger). The horizontal lines delimit the classes which are equivalent over the stronger theory PA⁻ + IΣ₀ + exp. It's indicated which principles are provable in RCA₀ (those below the thick dashed line).
to share – to copy, distribute and transmit the work
to remix – to adapt the work
Under the following conditions:
attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.