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Unprovability results involving braids

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Abstract
We construct long sequences of braids that are descending with respect to the standard order of braids (‘Dehornoy order’), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are not provable in the subsystems ISigma_1 or ISigma_2 of the standard Peano system (although they are provable in stronger systems of arithmetic).
Keywords
PROOF-THEORETIC ORDINALS, SEQUENCES, COMBINATORICS

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Citation

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

Chicago
Carlucci, Lorenzo , Patrick Dehornoy, and Andreas Weiermann. 2011. “Unprovability Results Involving Braids.” Ed. John Cremona and David Preiss. Proceedings of the London Mathematical Society 102 (3): 159–192.
APA
Carlucci, L., Dehornoy, P., & Weiermann, A. (2011). Unprovability results involving braids. (J. Cremona & D. Preiss, Eds.)PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 102(3), 159–192.
Vancouver
1.
Carlucci L, Dehornoy P, Weiermann A. Unprovability results involving braids. Cremona J, Preiss D, editors. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. 2011;102(3):159–92.
MLA
Carlucci, Lorenzo , Patrick Dehornoy, and Andreas Weiermann. “Unprovability Results Involving Braids.” Ed. John Cremona & David Preiss. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY 102.3 (2011): 159–192. Print.
@article{1246703,
  abstract     = {We construct long sequences of braids that are descending with respect to the standard order of braids ({\textquoteleft}Dehornoy order{\textquoteright}), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are not provable in the subsystems ISigma\_1 or ISigma\_2 of the standard Peano system (although they are provable in stronger systems of arithmetic).},
  author       = {Carlucci, Lorenzo  and Dehornoy, Patrick and Weiermann, Andreas},
  editor       = {Cremona, John and Preiss, David },
  issn         = {0024-6115},
  journal      = {PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY},
  keyword      = {PROOF-THEORETIC ORDINALS,SEQUENCES,COMBINATORICS},
  language     = {eng},
  number       = {3},
  pages        = {159--192},
  title        = {Unprovability results involving braids},
  url          = {http://dx.doi.org/10.1112/plms/pdq016},
  volume       = {102},
  year         = {2011},
}

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