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 σ1or σ2of the standard Peano system (although they are provable in stronger systems of arithmetic). © 2010 London Mathematical Society.
Unprovability results involving braids / Carlucci, Lorenzo; P., Dehornoy; A., Weiermann. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - STAMPA. - 102:1(2011), pp. 159-192. [10.1112/plms/pdq016]
Unprovability results involving braids
CARLUCCI, LORENZO;
2011
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 σ1or σ2of the standard Peano system (although they are provable in stronger systems of arithmetic). © 2010 London Mathematical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
