Recursion in total functionals of finite type

Solomon Feferman

Compositio Mathematica (1977)

  • Volume: 35, Issue: 1, page 3-22
  • ISSN: 0010-437X

How to cite

top

Feferman, Solomon. "Recursion in total functionals of finite type." Compositio Mathematica 35.1 (1977): 3-22. <http://eudml.org/doc/89333>.

@article{Feferman1977,
author = {Feferman, Solomon},
journal = {Compositio Mathematica},
language = {eng},
number = {1},
pages = {3-22},
publisher = {Noordhoff International Publishing},
title = {Recursion in total functionals of finite type},
url = {http://eudml.org/doc/89333},
volume = {35},
year = {1977},
}

TY - JOUR
AU - Feferman, Solomon
TI - Recursion in total functionals of finite type
JO - Compositio Mathematica
PY - 1977
PB - Noordhoff International Publishing
VL - 35
IS - 1
SP - 3
EP - 22
LA - eng
UR - http://eudml.org/doc/89333
ER -

References

top
  1. [1] S. Feferman: Ordinals and functionals in proof theory. Proc. Int'l. Cong. of Mathematicians (Nice, 1970) 1, 229-233. Zbl0244.02010MR437318
  2. [2] K. Gödel: Über einer bisher noch nicht benützten Erweiterung des finiten Standpunktes. Dialectica12 (1958) 280-287. Zbl0090.01003MR102482
  3. [3] T.J. Grilliot: Selection functions for recursive functionals. Notre Dame J. Formal Logic10 (1969) 225-234. Zbl0185.02302MR265152
  4. [4] L.A. Harrington and D.B. Macqueen: Selection in abstract recursion theory. J. Symbolic Logic41 (1976) 153-158. Zbl0409.03029MR441707
  5. [5] S.C. Kleene: Countable functionals, in Constructivity in Mathematics, N-H, Amsterdam (1959) 81-100. Zbl0100.24901MR112837
  6. [6] S.C. Kleene: Recursive functionals and quantifiers of finite types. Trans. Amer. Math. Soc.91 (1959) 1-52. Zbl0088.01301MR102480
  7. [7] G. Kreisel: Some reasons for generalizing recursion theory, in Logic Colloquium '69, N-H, Amsterdam (1971) 139-198. Zbl0219.02027MR321679
  8. [8] D.B. Macqueen: Post's problem for recursion in higher types. Dissertation, M.I.T. (1972). 
  9. [9] Y.N. Moschovakis: Hyperanalytic predicates. Trans. Amer. Math. Soc.129 (1967) 249-282. Zbl0159.01101MR236010
  10. [10] Y.N. Moschovakis: Abstract first order computability. Trans. Amer. Math. Soc.138 (1969) I. 427-464, II. 465-504. Zbl0218.02038MR244045
  11. [11] R. Platek: Foundations of recursion theory. Dissertation, Stanford Univ. (1966). 
  12. [12] G. Sacks: The 1-section of a type n object, in Generalized Recursion Theory (eds. Fenstad, Hinman), Amsterdam (1974) 81-93. Zbl0287.02026MR398811
  13. [13] J. Shoenfield: A hierarchy based on a type 2 object. Trans. Amer. Math. Soc.134 (1968) 103-108. Zbl0191.30502MR263626
  14. [14] W.W. Tait: Infinitely long terms of transfinite type, in Formal Systems and Recursive Functions, N-H, Amsterdam (1968) 465-475. 
  15. [15] S.S. Wainer: A hierarchy for the 1-section of any type two object, J. Symbolic Logic39 (1974) 88-94. Zbl0299.02048MR360244
  16. [16] H. Schwichtenberg and S.S. Wainer: Infinite terms and recursion in higher types. Kiel Proof Theory Symposion, 1974. Lecture Notes in Mathematics V. 500 (1975) (Springer, Berlin) 341-364. Zbl0341.02033MR419199

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.