Lesson plan
Elementary function arithmetic
In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, x^y , together with induction for formulas with bounded quantifiers. EFA is a very weak logical system, whose proof-theoretic ordinal is \omega^3 , but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.
Article summary
In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, x^y , together with induction for formulas with bounded quantifiers. EFA is a very weak logical system, whose proof-theoretic ordinal is \omega^3 , but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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