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Jason Rute
Jason Rute
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As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive recursion---really help to understand the program of reverse math. But also more advanced logic topics are useful. Computability theory and proof theory have already been mentioned. Knowing more about model theory helps, as does set theory (topics such as comprehension axioms, independence, descriptive set theory, and forcing offer insight into reverse mathematics).

Although having said that, after knowing the logical basics, it is quite possible to just jump into the subject and learn at least the main ideas of reverse mathematics. The first chapter of Subsystems of Second Order Arithmeticfirst chapter of Subsystems of Second Order Arithmetic is available on Steve Simpson's website. It is a good (and long) introduction to the basics of reverse mathematics. (It also may help one decide if they want to purchase the whole book.)

Last, reverse mathematics connects logic to other areas of mathematics. To understand say that "$\mathsf{ACA}_0$ is equivalent over $\mathsf{RCA}_0$ to the the Bolzano Weierstrass theorem", it is helpful to know the Bolzano Weierstrass theorem and a proof of it. In that direction, having a standard undergraduate mathematics education---real analysis, abstract algebra, topology, etc.---goes a long way.

As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive recursion---really help to understand the program of reverse math. But also more advanced logic topics are useful. Computability theory and proof theory have already been mentioned. Knowing more about model theory helps, as does set theory (topics such as comprehension axioms, independence, descriptive set theory, and forcing offer insight into reverse mathematics).

Although having said that, after knowing the logical basics, it is quite possible to just jump into the subject and learn at least the main ideas of reverse mathematics. The first chapter of Subsystems of Second Order Arithmetic is available on Steve Simpson's website. It is a good (and long) introduction to the basics of reverse mathematics. (It also may help one decide if they want to purchase the whole book.)

Last, reverse mathematics connects logic to other areas of mathematics. To understand say that "$\mathsf{ACA}_0$ is equivalent over $\mathsf{RCA}_0$ to the the Bolzano Weierstrass theorem", it is helpful to know the Bolzano Weierstrass theorem and a proof of it. In that direction, having a standard undergraduate mathematics education---real analysis, abstract algebra, topology, etc.---goes a long way.

As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive recursion---really help to understand the program of reverse math. But also more advanced logic topics are useful. Computability theory and proof theory have already been mentioned. Knowing more about model theory helps, as does set theory (topics such as comprehension axioms, independence, descriptive set theory, and forcing offer insight into reverse mathematics).

Although having said that, after knowing the logical basics, it is quite possible to just jump into the subject and learn at least the main ideas of reverse mathematics. The first chapter of Subsystems of Second Order Arithmetic is available on Steve Simpson's website. It is a good (and long) introduction to the basics of reverse mathematics. (It also may help one decide if they want to purchase the whole book.)

Last, reverse mathematics connects logic to other areas of mathematics. To understand say that "$\mathsf{ACA}_0$ is equivalent over $\mathsf{RCA}_0$ to the the Bolzano Weierstrass theorem", it is helpful to know the Bolzano Weierstrass theorem and a proof of it. In that direction, having a standard undergraduate mathematics education---real analysis, abstract algebra, topology, etc.---goes a long way.

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Jason Rute
Jason Rute
  • 6.3k
  • 2
  • 30
  • 53

As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive recursion---really help to understand the program of reverse math. But also more advanced logic topics are useful. Computability theory and proof theory have already been mentioned. Knowing more about model theory helps, as does set theory (topics such as comprehension axioms, independence, descriptive set theory, and forcing offer insight into reverse mathematics).

Although having said that, after knowing the logical basics, it is quite possible to just jump into the subject and learn at least the main ideas of reverse mathematics. The first chapter of Subsystems of Second Order Arithmetic is available on Steve Simpson's website. It is a good (and long) introduction to the basics of reverse mathematics. (It also may help one decide if they want to purchase the whole book.)

Last, reverse mathematics connects logic to other areas of mathematics. To understand say that "$\mathsf{ACA}_0$ is equivalent over $\mathsf{RCA}_0$ to the the Bolzano Weierstrass theorem", it is helpful to know the Bolzano Weierstrass theorem and a proof of it. In that direction, having a standard undergraduate mathematics education---real analysis, abstract algebra, topology, etc.---goes a long way.