Relative To Any Nonrecursive Set

Relative To Any Nonrecursive Set (1996)

by Theodore Slaman

Venue:	Proc. Amer. Math. Soc
Citations:	15 - 0 self

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Datum	Value	Source
TITLE	Relative To Any Nonrecursive Set	user correction - Legacy Corrections
AUTHOR NAME	Theodore Slaman	user correction - Legacy Corrections
ABSTRACT	. There is a countable first order structure M such that for any set of integers X, X is not recursive if and only if there is a presentation of M which is recursive in X. 1. Introduction It is a well-known truth that if a set R ` ! is recursive relative to every nonrecursive subset of !, then R is recursive (see [Kleene and Post, 1954]). Similarly, if R is recursive in every element of a co-meager set, then R is recursive; if R is recursive in every element of a set of positive measure, then R is recursive; and if R is recursive in every element of a nonempty \Pi 0 1 set P , then R is recursive in the real appearing in the definition of P . In fact, one can consider a wide variety of notions of forcing P, and conclude that if R is recursive in every generic set (extending the condition p), then R is recursive in P (and p). Thus, in wide generality, there is no R ` ! which constitutes information common to all nonrecursive reals or to all generic reals. Even so, one need not abando...	user correction - Legacy Corrections
YEAR	1996	user correction - Legacy Corrections
VENUE	Proc. Amer. Math. Soc	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2117--2122	INFERENCE
VOLUME	126	INFERENCE
CITATIONS	1 found	ParsCit 1.0