Reverse mathematics: the playground of logic

@article{Shore2010ReverseMT,
  title={Reverse mathematics: the playground of logic},
  author={Richard A. Shore},
  journal={Bulletin of Symbolic Logic},
  year={2010},
  volume={16},
  pages={378-402}
}
The general enterprise of calibrating the strength of classical mathematical theorems in terms of the axioms (typically of set existence) needed to prove them was begun by Harvey Friedman in [1971] (see also [1967]). His goals were both philosophical and foundational. What existence assumptions are really needed to develop classical mathematics and what other axioms and methods suffice to carry out standard constructions and proofs? In the [1971] paper, Friedman worked primarily in the set… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 64 references

Necessary uses of Σ11 induction in a reversal

  • I. Neeman
  • 2012

The Homogeneous Model Theorem, in preparation

  • D. R. Hirschfeldt, K. Lange, R. A. Shore
  • 2012

Proofs and Computations, Perspectives in Logic, Association for Symbolic Logic and

  • H. Schwichtenberg, S. Wainer
  • 2011

Reverse mathematics and well-ordering principles, to appear

  • M. Rathjen, A. Weiermann
  • 2011

The limits of determinacy in second order arithmetic

  • A. Montalbán, R. A. Shore
  • 2011

[ 1999 ] , Defining the Turing jump

  • R. A. Shore, T. A. Slaman
  • Math . Research Letters
  • 2011

On the role of the Collection Principle for Σ 02 - formulas in second - order reverse mathematics

  • C. T. Chong, S. Lempp
  • Proceedings of the American Mathematical Society
  • 2010

Similar Papers

Loading similar papers…