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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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