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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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SUBSTRUCTURE LATTICES

SUBSTRUCTURE LATTICES

Chapter:
(p.89) 4 SUBSTRUCTURE LATTICES
Source:
The Structure of Models of Peano Arithmetic
Author(s):

Roman Kossak

James H. Schmerl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568278.003.0004

This chapter examines substructure lattices, with emphasis on how to obtain models with specific finite lattices as substructure lattices. The finite distributive lattice case is presented in full. The general technique involving canonical partition properties using congruence lattices and theorems such as the Hales-Jewett theorem is described and applied. Wilkie's theorem for the pentagon lattice and Paris' theorem for all countable distributive lattices are also presented.

Keywords:   Hales-Jewett theorem, Wilkie's theorem, interstructure lattice, canonical partition property

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