Tiered Arithmetic and its Applications - Çagman, Naim;Wainer, Stan S.
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This book is first author's dissertation that is submitted in accordance with the requirements for the degree of Doctor of Philosophy to The University of Leeds, Department of Pure Mathematics in January 2000 under the direction of second author with the title "Tiered Arithmetic, its Functional Interpretation and Slow Growing Bounds". A two-sorted version of Peano Arithmetic is developed, with proof-rules corresponding to the normal/safe recursion schemes of Bellantoni and Cook. Classical methods of proof theory still apply, but now the provably recursive functions are brought down to more…mehr

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Produktbeschreibung
This book is first author's dissertation that is submitted in accordance with the requirements for the degree of Doctor of Philosophy to The University of Leeds, Department of Pure Mathematics in January 2000 under the direction of second author with the title "Tiered Arithmetic, its Functional Interpretation and Slow Growing Bounds". A two-sorted version of Peano Arithmetic is developed, with proof-rules corresponding to the normal/safe recursion schemes of Bellantoni and Cook. Classical methods of proof theory still apply, but now the provably recursive functions are brought down to more computationally realistic levels than in the single-sorted case, since the bounding functions turn out to be "slow growing" rather than "fast growing". Result very similar to earlier ones of Leivant are obtained characterizing Grzegorczyk s classes (in the existential fragment) and (in the full theory).
Autorenporträt
Naim Çäman received his BSc from the Istanbul University in 1991, MSc from the Wales Swansea University in 1996, PhD from the Leeds University in 2000. Since 2000, he has been working on the mathematical logic at the Gaziosmanpasa University. Please visit his website http://idak.gop.edu.tr/ncagman/index-e.htm for more information.