[FOM] PA inconsistencies

[Sam Sanders]

Dear Harvey,

> FOM Readership: what are the main references for "mathematics without
> exponentiation" and how far has it gotten?

A major contribution is Nelson’s book “predicative arithmetic” and outgrowths. 

However, this approach has its problems: there exist (fairly natural) statements A, B
such that both A and B are acceptable acceptable in Nelson’s framework, but A AND B
is not acceptable.  

Also, there are a number of people that have done “feasible reverse math”, i.e. reverse
math over a base theory weaker than EFA.  

Finally, when one does “mathematics without exponentiation”, I believe statements become
very sensitive to coding.  

Best,

Sam