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}


  1. On notions of computability theoretic reductions between Pi12 principles by Hirschfeld and Jockusch. This one is about using interesting axioms.

  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. OR provephp.pdf

  3. Proving infinitude of primes numbers using binominal coefficients by Phuong Nguyen.

  4. Bounded Reverse Math (Slides for a talk)