| Ramified Frege Arithmetic |
| Richard Heck |
| forthcoming in the Journal of Philosophical Logic |
| Area 1 Philosophy of Mathematics |
| Area 2 Logic |
| Keywords Frege arithmetic HP predicativity |
| http://frege.brown.edu/heck/pdf/unpublished/RamifiedFregeArithmetic.pdf |
| http://frege.brown.edu/heck/pdf/unpublished/RamifiedFregeArithmetic.ps |
| Oystein Linnebo has shown that the existence of successors cannot be proven in predicative Frege arithmetic, that is, predicative second-order logic plus "Hume's Principle" and Frege's definitions of zero, predecessor, and natural number. It is shown in the present paper that the existence of successors can be proven if the logic is strengthened to ramified predicative second-order logic. It then follows from work by John Burgess and Allen Hazen that Robinson arithmetic, Q, can be interpreted in ramified Frege arithmetic. |
This site makes heavy use of CSS and some use of the DOM and JavaScript.
It is strongly recommended that you use a current standards-compliant browser to view it, such as Firefox.
If you are having difficulties with the site, please write the maintainer and include your User Agent string, which is:
CCBot/1.0 (+http://www.commoncrawl.org/bot.html)
Have a nice day.
