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Scott's problem for Proper Scott sets

Published online by Cambridge University Press:  12 March 2014

Victoria Gitman*
Affiliation:
New York City College of Technology (Cuny), Mathematics, 300 Jay Street, Brooklyn, NY 11201, USA, E-mail: vgitman@nylogic.org

Abstract

Some 40 years ago, Dana Scott proved that every countable Scott set is the standard system of a model of PA. Two decades later, Knight and Nadel extended his result to Scott sets of size ω1. Here, I show that assuming the Proper Forcing Axiom (PFA), every A-proper Scott set is the standard system of a model of PA. I define that a Scott set is proper if the quotient Boolean algebra /Fin is a proper partial order and A-proper if is additionally arithmetically closed. I also investigate the question of the existence of proper Scott sets.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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