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The Structure of Models of Peano Arithmetic$
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Roman Kossak and James Schmerl

Print publication date: 2006

Print ISBN-13: 9780198568278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568278.001.0001

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(p.256) 10 ω1-LIKE MODELS
The Structure of Models of Peano Arithmetic

Roman Kossak

James H. Schmerl

Oxford University Press

This chapter presents several constructions of ω1-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated models, models whose additive reducts are isomorphic but whose multiplicative reducts are not, and very similar but nonisomorphic models. The chapter also presents two constructions used in completeness theorems for Peano Arithmetic with the Ramsey quantifier and the stationary quantifier.

Keywords:   rather classless model, rigid model, additive reduct, multiplicative reduct, Ramsey quantifier, stationary logic

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