In:
Journal of Symbolic Logic, Cambridge University Press (CUP), Vol. 47, No. 2 ( 1982-06), p. 416-422
Abstract:
Flipping properties were introduced in set theory by Abramson, Harrington, Kleinberg and Zwicker [1]. Here we consider them in the context of arithmetic and link them with combinatorial properties of initial segments of nonstandard models studied in [3] . As a corollary we obtain independence resutls involving flipping properties. We follow the notation of the author and Paris in [3] and [2] , and assume some knowledge of [3]. M will denote a countable nonstandard model of P (Peano arithmetic) and I will be a proper initial segment of M . We denote by N the standard model or the standard part of M. X ↑ I will mean that X is unbounded in I . If X ⊆ M is coded in M and M ≺ K , let X (K) be the subset of K coded in K by the element which codes X in M . So X (K) ⋂ M = X . Recall that M ≺ I K ( K is an I -extension of M ) if M ≺ K and for some c ∈ K , In [3] regular and strong initial segments are defined, and among other things it is shown that I is regular if and only if there exists an I -extension of M .
Type of Medium:
Online Resource
ISSN:
0022-4812
,
1943-5886
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1982
detail.hit.zdb_id:
3077-6
detail.hit.zdb_id:
2010607-5
SSG:
5,1
SSG:
17,1
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