{"product_id":"tiered-arithmetic-and-its-applications-von-naim-cagman-und-stan-s-wainer","title":"Tiered Arithmetic and its Applications","description":"\u003cp\u003eThis 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).\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838365619\"\u003e\u003ch3\u003eTiered arithmetic, its functional interpretation and slow growing bounds\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838365619","offer_id":39499032723549,"sku":"9783838365619","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/e896c9a9-d4f2-4fed-89d3-52eaf8590bc4.jpg?v=1773382992","url":"https:\/\/shop.autorenwelt.de\/en\/products\/tiered-arithmetic-and-its-applications-von-naim-cagman-und-stan-s-wainer","provider":"Autorenwelt Shop","version":"1.0","type":"link"}