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Menger's theorem in Pi(1)(1)-CA(0)

Paul Shafer (UGent)
(2012) ARCHIVE FOR MATHEMATICAL LOGIC. 51(3-4). p.407-423
Author
Organization
Abstract
We prove Menger's theorem for countable graphs in Pi(1)(1)-CA(0). Our proof in fact proves a stronger statement, which we call extended Menger's theorem, that is equivalent to Pi(1)(1)-CA(0) over RCA(0).
Keywords
Graph theory, Reverse mathematics, Matching theory, KONIG DUALITY THEOREM, INFINITE BIPARTITE GRAPHS, STRENGTH

Citation

Please use this url to cite or link to this publication:

MLA
Shafer, Paul. “Menger’s Theorem in Pi(1)(1)-CA(0).” ARCHIVE FOR MATHEMATICAL LOGIC, vol. 51, no. 3–4, 2012, pp. 407–23, doi:10.1007/s00153-012-0269-8.
APA
Shafer, P. (2012). Menger’s theorem in Pi(1)(1)-CA(0). ARCHIVE FOR MATHEMATICAL LOGIC, 51(3–4), 407–423. https://doi.org/10.1007/s00153-012-0269-8
Chicago author-date
Shafer, Paul. 2012. “Menger’s Theorem in Pi(1)(1)-CA(0).” ARCHIVE FOR MATHEMATICAL LOGIC 51 (3–4): 407–23. https://doi.org/10.1007/s00153-012-0269-8.
Chicago author-date (all authors)
Shafer, Paul. 2012. “Menger’s Theorem in Pi(1)(1)-CA(0).” ARCHIVE FOR MATHEMATICAL LOGIC 51 (3–4): 407–423. doi:10.1007/s00153-012-0269-8.
Vancouver
1.
Shafer P. Menger’s theorem in Pi(1)(1)-CA(0). ARCHIVE FOR MATHEMATICAL LOGIC. 2012;51(3–4):407–23.
IEEE
[1]
P. Shafer, “Menger’s theorem in Pi(1)(1)-CA(0),” ARCHIVE FOR MATHEMATICAL LOGIC, vol. 51, no. 3–4, pp. 407–423, 2012.
@article{7175895,
  abstract     = {{We prove Menger's theorem for countable graphs in Pi(1)(1)-CA(0). Our proof in fact proves a stronger statement, which we call extended Menger's theorem, that is equivalent to Pi(1)(1)-CA(0) over RCA(0).}},
  author       = {{Shafer, Paul}},
  issn         = {{1432-0665}},
  journal      = {{ARCHIVE FOR MATHEMATICAL LOGIC}},
  keywords     = {{Graph theory,Reverse mathematics,Matching theory,KONIG DUALITY THEOREM,INFINITE BIPARTITE GRAPHS,STRENGTH}},
  language     = {{eng}},
  number       = {{3-4}},
  pages        = {{407--423}},
  title        = {{Menger's theorem in Pi(1)(1)-CA(0)}},
  url          = {{http://doi.org/10.1007/s00153-012-0269-8}},
  volume       = {{51}},
  year         = {{2012}},
}

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