T. Arai. A slow growing analogue to Buchholz' proof. Annals of Pure and Applied Logic, 54:101-120, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....provable in KP i n can be proven in ML i 1 WR as well. There are some ideas, using the well ordering proof to do this. From there might follow, too, some bounds for the fast or slow growing hierarchy (see for instance proof theoretical work on this in [Sch77b] Sch92c] BW87] Wai89] [Ara91], Buc91b] Buc91a] Remark: While the author was finishing his thesis, M. Rathjen has told him, that in collaboration with E. Gri#or independently and in parallel he has found similar results, although he has not submitted it for publication, yet, or told anything to the author. ....

T. Arai. A slow growing analogue to Buchholz' proof. Ann. Pure a. Appl. Logic, 54:101 -- 120, 1991.

....of ff by: 0[n] ff 1) n] ff[n] fffg, hff x i[n] ff n [n] Then ff[n] is easily seen to be linearly ordered by . 1.4. Definition. ff 2 Omega 1 is said to be structured if it is presented as the directed union of its finite subsets ff[n] as follows: i) ff[0] ff[1] ff[2] : ii) fi ff ( 9n 2 N (fi 2 ff[n] Thus if ff is structured, ffi: fi ffg is well ordered with least element 0 and such that fi ff = fi 1 ff. Ordinal Bounds for Programs 381 1.5. Remark. Although we have not placed any effectivity conditions on the formation of ....

T. Arai. A slow growing analogue to Buchholz' proof. Annals of Pure and Applied Logic, 54:101--120, 1991.

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T. Arai. A slow growing analogue to Buchholz' proof. Annals of Pure and Applied Logic, 54:101-120, 1991.

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