The proof theoretic strength of the Steinitz exchange theorem

نویسنده

  • Michael Soltys
چکیده

We show that the logical theory QLA proves the Cayley–Hamilton theorem from the Steinitz exchange theorem together with a strengthening of the linear independence principle. Since QLA is a fairly weak theory (in the sense that its quantifier-free fragment, LA, translates into tautologies with TC0-Frege proofs—when restricted to the field Q of the rationals), it follows that the proof complexity of matrix algebra can be distilled to the Steinitz exchange theorem. © 2006 Elsevier B.V. All rights reserved.

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عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 155  شماره 

صفحات  -

تاریخ انتشار 2007