An independence result for (II11-CA)+BI

نویسنده

  • Wilfried Buchholz
چکیده

In Kirby and Paris [5] it was shown that a certain combinatorial statement (conceming finite trees) is independent of Peano Arithmetic. Here we present a not too complicated extension of tbis statement and prove its independence from the riluch stronger theory (II~-CA) + BI. This is done by refining the methods which we have developed in [2, Ch. IV, §1-§4]. Using the terminology of Kirby and Paris our result can be described as follows. A hydra is a finite labeled tree A which has the following properties: (i) the root of A has label +, (ii) any other node of A is labeled by some ordinal v ~ ro, (iü) all nodes immediately above the root of A have label 0 (zero). If Hereules chops off a head (i.e. top node) a of a given hydra A, the hydra will choose an arbitrary number n E N and transform itself into a new hydra A( a, n) as follows. Let T denote that node of A wbich is immediately below a, and let A denote that part of A which remains after a has been chopped off. The definition of A( a, n) depends on the label of a: Case 1: label (a) =0. H T is the root of A, we set A(a, n):=A-. Otherwise A( a, n) results from A by sprouting n replicas of A; from the node immediately below T. Here A; denotes the subtree of A determined by T.

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عنوان ژورنال:
  • Ann. Pure Appl. Logic

دوره 33  شماره 

صفحات  -

تاریخ انتشار 1987