Reverse mathematics of some topics from algorithmic graph theory
Fundamenta Mathematicae (1998)
- Volume: 157, Issue: 1, page 1-13
- ISSN: 0016-2736
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Abstract
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topClote, Peter, and Hirst, Jeffry. "Reverse mathematics of some topics from algorithmic graph theory." Fundamenta Mathematicae 157.1 (1998): 1-13. <http://eudml.org/doc/212275>.
@article{Clote1998,
abstract = {This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.},
author = {Clote, Peter, Hirst, Jeffry},
journal = {Fundamenta Mathematicae},
keywords = {reverse mathematics; proof theory; recursion theory; graph theory; reachability matrices; topological sorting; spanning trees},
language = {eng},
number = {1},
pages = {1-13},
title = {Reverse mathematics of some topics from algorithmic graph theory},
url = {http://eudml.org/doc/212275},
volume = {157},
year = {1998},
}
TY - JOUR
AU - Clote, Peter
AU - Hirst, Jeffry
TI - Reverse mathematics of some topics from algorithmic graph theory
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 1
SP - 1
EP - 13
AB - This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.
LA - eng
KW - reverse mathematics; proof theory; recursion theory; graph theory; reachability matrices; topological sorting; spanning trees
UR - http://eudml.org/doc/212275
ER -
References
top- [1] J. Hirst, Combinatorics in subsystems of second order arithmetic, Ph.D. Thesis, The Pennsylvania State University, 1987.
- [2] J. Hirst, Connected components of graphs and reverse mathematics, Arch. Math. Logic 31 (1992), 183-192. Zbl0725.03039
- [3] S. Simpson, Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?, J. Symbolic Logic 49 (1984), 783-802. Zbl0584.03039
- [4] S. Simpson, Subsystems of , in: Proof Theory, G. Takeuti (ed.), North-Holland, Amsterdam, New York, 1985, 434-448.
- [5] R. Soare, Recursively Enumerable Sets and Degrees, Springer, Berlin, 1987.
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