Ordinal analysis of bar recursion of type zero

W. A. Howard

Compositio Mathematica (1980)

  • Volume: 42, Issue: 1, page 105-119
  • ISSN: 0010-437X

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Howard, W. A.. "Ordinal analysis of bar recursion of type zero." Compositio Mathematica 42.1 (1980): 105-119. <http://eudml.org/doc/89466>.

@article{Howard1980,
author = {Howard, W. A.},
journal = {Compositio Mathematica},
keywords = {computation trees; transfinite recursion; terms for functionals of finite type; bar recursion of type zero; ordinal notations; elementary intuitionistic analysis; Skolem arithmetic},
language = {eng},
number = {1},
pages = {105-119},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Ordinal analysis of bar recursion of type zero},
url = {http://eudml.org/doc/89466},
volume = {42},
year = {1980},
}

TY - JOUR
AU - Howard, W. A.
TI - Ordinal analysis of bar recursion of type zero
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 42
IS - 1
SP - 105
EP - 119
LA - eng
KW - computation trees; transfinite recursion; terms for functionals of finite type; bar recursion of type zero; ordinal notations; elementary intuitionistic analysis; Skolem arithmetic
UR - http://eudml.org/doc/89466
ER -

References

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  1. [1] H. Gerber: An extension of Schütte's Klammersymbols. Mathematische Annalen, 174 (1967), 203-216. Zbl0162.01901MR223246
  2. [2] H. Gerber, Brouwer's bar theorem and a system of ordinal notations. Proceedings of the Summer Conference on Intuitionism and Proof Theory. North-Holland, Amsterdam, 1970. Zbl0205.01103MR280334
  3. [3] W. Howard, Functional interpretation of bar induction by bar recursion. Compositio Mathematica20 (1968) 107--124. Zbl0162.31503MR230619
  4. [4] W. Howard, A system of abstract ordinals. Journal of Symbolic Logic, 37 (1972) 355-374. Zbl0264.02026MR329869
  5. [5] W. Howard, Ordinal analysis of terms of finite type, (to appear). Zbl0444.03029MR583368
  6. [6] W. Howard, Ordinal analysis of simple cases of bar recursion, (to appear). Zbl0463.03031MR604874
  7. [7] H. Vogel, Über die mit dem Bar-Rekursor vom Type 0 definierbaren Ordinalzahlen. Archiv für Mathematische Logik und Grundlagenforschung19 (1978) 139-156. Zbl0414.03034MR539870

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