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The Structure of Models of Peano Arithmetic

Roman Kossak and James Schmerl

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, ... More


EPISTEMIC CAUSALITY

Jon Williamson

in Bayesian Nets and Causality: Philosophical and Computational Foundations

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530794
eISBN:
9780191712982
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530794.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and ... More


ω1-LIKE MODELS

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

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 ... More


HOW TO CONTROL TYPES

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of ... More


Synchronizing Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter considers a new type of graph coloring known as edge coloring. It begins with a discussion of an idea by Scottish physicist Peter Guthrie Tait that led to edge coloring. Tait proved that ... More


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