| Title:
|
The limit lemma in fragments of arithmetic (English) |
| Author:
|
Švejdar, Vítězslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
565-568 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The recursion theoretic limit lemma, saying that each function with a $\varSigma_{n+2}$ graph is a limit of certain function with a $\varDelta_{n+1}$ graph, is provable in $\text{\rm B}\Sigma_{n+1}$. (English) |
| Keyword:
|
limit lemma |
| Keyword:
|
fragments of arithmetic |
| Keyword:
|
collection scheme |
| MSC:
|
03D20 |
| MSC:
|
03D55 |
| MSC:
|
03F30 |
| idZBL:
|
Zbl 1098.03067 |
| idMR:
|
MR2025821 |
| . |
| Date available:
|
2009-01-08T19:31:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119409 |
| . |
| Reference:
|
[1] Clote P.: Partition relations in arithmetic.in C.A. DiPrisco, Ed., {Methods in Mathematical Logic}, Lecture Notes in Mathematics 1130, Springer, 1985, pp.32-68. Zbl 0567.03029, MR 0799036 |
| Reference:
|
[2] Hájek P., Kučera A.: On recursion theory in $I{\Sigma_1}$.J. Symbolic Logic 54 (1989), 576-589. MR 0997890 |
| Reference:
|
[3] Hájek P., Pudlák P.: Metamathematics of First Order Arithmetic.Springer, 1993. MR 1219738 |
| Reference:
|
[4] Kučera A.: An alternative, priority-free, solution to Post's problem.in J. Gruska, B. Rovan, and J. Wiedermann, Eds., {Mathematical Foundations of Computer Science 1986} (Bratislava, Czechoslovakia, August 25-29, 1986), Lecture Notes in Computer Science 233, Springer, 1986, pp.493-500. Zbl 0615.03033, MR 0874627 |
| Reference:
|
[5] Rogers H., Jr.: Theory of Recursive Functions and Effective Computability.McGraw-Hill, New York, 1967. Zbl 0256.02015, MR 0224462 |
| . |
