On provably recursive functions and ordinal recursive functions*
نویسندگان
چکیده
منابع مشابه
Induction rules re ection principles and provably recursive functions
A well known result states that over basic Kalmar elementary arith metic EA the induction schema for n formulas is equivalent to the uniform re ection principle for n formulas n We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of re ection principles as well Thus the closure of EA under the induction rule for n or n for...
متن کاملInduction Rules, Reflection Principles, and Provably Recursive Functions
A well known result of D Leivant states that over basic Kalmar ele mentary arithmetic EA the induction schema for n formulas is equivalent to the uniform re ection principle for n formulas We show that frag ments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of re ection principles as well Thus the closure of EA under the induction rule fo...
متن کاملInduction Rules, Reeection Principles, and Provably Recursive Functions
A well-known result of D. Leivant states that, over basic Kalmar elementary arithmetic EA, the induction schema for n formulas is equivalent to the uniform reeection principle for n+1 formulas. We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reeection principles as well. Thus, the closure of EA under the induction r...
متن کاملRamsey's Theorem for Pairs and Provably Recursive Functions
This paper addresses the strength of Ramsey’s theorem for pairs (RT2) over a weak base theory from the perspective of ‘proof mining’. Let RT2− 2 denote Ramsey’s theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König’s lemma and a substantial amount of Σ1-induction (enough to prove t...
متن کاملReal Recursive Functions and Real Extensions of Recursive Functions
Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1968
ISSN: 0025-5645
DOI: 10.2969/jmsj/02030456