Combinatorial functions and regressive isols
نویسندگان
چکیده
منابع مشابه
Hereditarily Odd–even and Combinatorial Isols
In this paper we study some of the arithmetic structure that is found in a special kind of semi-ring in the isols. These are the semi-rings [D(Y ),+, ·] that were introduced by J.C.E. Dekker, and that were later shown by E. Ellentuck to model the true universal recursive statements of arithmetic when Y is a regressive isol and is hyper-torre (= hereditarily odd-even = HOE). When Y is regressive...
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We compute an explicit upper bound for the regressive Ramsey numbers by a combinatorial argument, the corresponding function being of Ackermannian growth. For this, we look at the more general problem of bounding g(n,m), the least l such that any regressive function f : [m, l] → N admits a min-homogeneous set of size n. Analysis of this function also leads to the simplest known proof that the r...
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The universal isol metatheorem is extended so as to deal with nonrecursive relations and countable Boolean operations.
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Motivated by a conjecture of Ellentuck concerning fibers f^x(C), f recursive and C an element of one of Barback's "tame models" (Tame models in the isols, Houston J. Math. 12 (1986), 163-175), we study such fibers in the more general context of Nerode semirings. The principal results are that (1) all existentially complete Nerode semirings meet all of their recursive fibers, and (2) not all Ner...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1963
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1963.13.703