∑1 definitions with parameters

Journal of Symbolic Logic 51 (2):453-461 (1986)
  Copy   BIBTEX

Abstract

Let p be a set. A function φ is uniformly σ 1 (p) in every admissible set if there is a σ 1 formula φ in the parameter p so that φ defines φ in every σ 1 -admissible set which includes p. A theorem of Van de Wiele states that if φ is a total function from sets to sets then φ is uniformly σ 1R in every admissible set if anly only if it is E-recursive. A function is ES p -recursive if it can be generated from the schemes for E-recursion together with a selection scheme over the transitive closure of p. The selection scheme is exactly what is needed to insure that the ES p - recursively enumerable predicates are closed under existential quantification over the transitive closure of p. Two theorems are established: a) If the transitive closure of p is countable than a total function on sets is ES p -recursive if and only if it is uniformly σ 1 (p) in every admissible set. b) For any p, if φ is a function on the ordinal numbers then φ is ES p -recursive if and only if it is uniformly ∑ 1 (p) in every admissible set

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,378

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Pornographic Art - A Case from Definitions.Simon Fokt - 2012 - British Journal of Aesthetics 52 (3):287-300.
Defining Philosophical Counselling: An Overview1.D. Louw - 2013 - South African Journal of Philosophy 32 (1):60-70.
Locus equation and hidden parameters of speech.Li Deng - 1998 - Behavioral and Brain Sciences 21 (2):263-264.
An Inquiry into the Definitions of the Possible.Aynullah Khademi - unknown - Kheradnameh Sadra Quarterly 37.
On definitions of consciousness.Anders Sogaard & Stine Osterskov Sogaard - 2009 - Journal of Consciousness Studies 16 (5):46-53.
Kant on real definitions in geometry.Jeremy Heis - 2014 - Canadian Journal of Philosophy 44 (5-6):605-630.

Analytics

Added to PP
2009-01-28

Downloads
40 (#342,506)

6 months
1 (#1,005,371)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Another extension of Van de Wiele's theorem.Robert S. Lubarsky - 1988 - Annals of Pure and Applied Logic 38 (3):301-306.

Add more citations

References found in this work

Narrow boolean algebras.Robert Bonnet & Saharon Shelah - 1985 - Annals of Pure and Applied Logic 28 (1):1-12.
Preface.Klaus Ambos-Spies, Theodore A. Slaman & Robert I. Soare - 1998 - Annals of Pure and Applied Logic 94 (1-3):1.

Add more references