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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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GENERICS AND FORCING

GENERICS AND FORCING

Chapter:
(p.158) 6 GENERICS AND FORCING
Source:
The Structure of Models of Peano Arithmetic
Author(s):

Roman Kossak

James H. Schmerl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568278.003.0006

This chapter provides a brief introduction to forcing in models of PA, and includes some applications. It is proved that in general the MacDowell-Specker Theorem does not hold for uncountable languages. However, in some situations it does producing models with many generic classes. Perfect forcing is used to show that countable languages can, in some sense, be replaced by finite languages.

Keywords:   generics, forcing, MacDowell-Specker Theorem, Cohen forcing, perfect generics

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