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September 2008 Scott’s problem for Proper Scott sets
Victoria Gitman
J. Symbolic Logic 73(3): 845-860 (September 2008). DOI: 10.2178/jsl/1230396751

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 𝔛 is proper if the quotient Boolean algebra 𝔛/Fin is a proper partial order and A-proper if 𝔛 is additionally arithmetically closed. I also investigate the question of the existence of proper Scott sets.

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Victoria Gitman. "Scott’s problem for Proper Scott sets." J. Symbolic Logic 73 (3) 845 - 860, September 2008. https://doi.org/10.2178/jsl/1230396751

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1161.03024
MathSciNet: MR2444272
Digital Object Identifier: 10.2178/jsl/1230396751

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 3 • September 2008
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