Papers on Logical Systems

These are papers on logical system that I hope can help me formulate a reverse mathematics below the level of {rm RCA}_0.

Here is a test: RCA_0^1 and sum_{i=0}^n

HEre is a bolder test

 sum_{i=1}^n i =frac{n(n+1)}{2}

Papers

  1. On notions of computability theoretic reductions between Pi12 principles by Hirschfeld and Jockusch. This one is about using interesting axioms. http://math.uchicago.edu/~drh/Papers/upaper.html

  2. Provability of the Pigeonhole principle and the existence of infinitely many primes by Paris, Wilkie, Woods. JSL Vol 53, 1988, 1235-1244. Show that from IDelta0 + Omega1 you can get infinitely manh primes. Combines Diag with a construction similar to the construction used later to form a psuedorandom function gen from a p-random number generator. http://www.jstor.org/stable/pdf/2274618.pdf?acceptTC=true OR provephp.pdf

  3. Proving infinitude of primes numbers using binominal coefficients by Phuong Nguyen. http://www.cs.toronto.edu/~pnguyen/studies/prime.pdf

  4. Bounded Reverse Math (Slides for a talk)

https://www.cs.toronto.edu/~sacook/banff_survey.pdf