## The Regress Objection

*Alexander Bird*

### in Nature's Metaphysics: Laws and Properties

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199227013
- eISBN:
- 9780191711121
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227013.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology

It is often claimed (e.g., by Swinburne, Armstrong, and Lowe) that the view that all natural properties are potencies leads to a vicious regress or circularity. The possible interpretations of this ... More

## PENTAD GROUP 23+12 · (L 3(2) × Sym5)

*A. A. Ivanov*

### in The Fourth Janko Group

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.003.0004
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses the geometric subgroup at level 2 of the modified amalgam G, known as the pentad group, which has a rather complicated structure. The structure can be described in terms of the ... More

## TOWARDS 2 + 1 + 12 · 3 · Aut ( M 22 )

*A. A. Ivanov*

### in The Fourth Janko Group

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.003.0005
- Subject:
- Mathematics, Pure Mathematics

This chapter shows that N[3] is the extraspecial group Q[3] ≅ 21+12 + extended by a group R of order 3 acting fixed-point freely on Q[3]/Z[3] (where Z[3] is the centre of Q[3]/) and ... More

## INTRODUCTION

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up ... More

## THE STRUCTURE OF COMPOSITION

*Pavol Hell and Jaroslav Nešetřil*

### in Graphs and Homomorphisms

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0004
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the structure, as opposed to just the existence, of the family of homomorphisms among a set of graphs. The difference is noticeable with even just one graph. For instance, a ... 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

## AUTOMORPHISMS OF RECURSIVELY SATURATED 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/9780198568278.003.0008
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops the basic theory of automorphisms of countable recursively saturated models of PA. The key results are: Smoryìnski's characterization of exponentially closed cuts, the Moving ... More

## The Invention of Tradition and Social Memory 1

*BARBARA CZARNIAWSKA*

### in A Tale of Three Cities: Or the Glocalization of City Management

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780199252718
- eISBN:
- 9780191719295
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252718.003.0005
- Subject:
- Business and Management, International Business

The difficulties in effective city management in Warsaw did not stem from its communist past but from a veneered sedimentation of a rationalist-legalist frame of action. This chapter discusses ... More

## The center and outer automorphisms of Spin(n)

*Adam M. Bincer*

### in Lie Groups and Lie Algebras: A Physicist's Perspective

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199662920
- eISBN:
- 9780191745492
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662920.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Center and inner and outer automorphisms are defined. The chapter shows that the center of Spin(n) consists of two elements for n odd, and 4 elements for n even. More precisely the center has the ... More

## Classification of Pseudo-reductive Groups (AM-191)

*Brian Conrad and Gopal Prasad*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167923
- eISBN:
- 9781400874026
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167923.001.0001
- Subject:
- Mathematics, Numerical Analysis

This book goes further than the exploration of the general structure of pseudo-reductive groups to study the classification over an arbitrary field. An Isomorphism Theorem proved here determines the ... More

## Fixed Apartments

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0025
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the conditions which force a group of order 2 acting on a building to stabilize various kinds of substructures. It shows that a group of order 2 acting on a spherical building ... More

## Galois Involutions

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0031
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the fixed points of a strictly semi-linear automorphism of order 2 of a spherical building which satisfies the conditions laid out in Hypothesis 30.1. It begins with the fhe ... More

## Automorphisms, isomorphisms, and Tits classification

*Brian Conrad and Gopal Prasad*

### in Classification of Pseudo-reductive Groups (AM-191)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167923
- eISBN:
- 9781400874026
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167923.003.0006
- Subject:
- Mathematics, Numerical Analysis

This chapter considers automorphisms, isomorphisms, and Tits classification. It begins by establishing a version of the Isomorphism Theorem for pseudo-split pseudo-reductive groups, along with a ... More

## Fermionic Dynamical Systems

*Robert Alicki and Mark Fannes*

### in Quantum Dynamical Systems

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on the mathematical description of Fermionic systems. It first describes the usual formalism of second quantization in terms of operators on anti-symmetric Fock space. It then ... More

## Ergodic Theory

*Robert Alicki and Mark Fannes*

### in Quantum Dynamical Systems

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter defines and characterizes various degrees of ergodicity — both for classical and quantum systems — in terms of the Hilbert space formalism, Koopman formalism for classical systems, and ... More

## Automorphisms of Free Groups

*Matt Clay*

### in Office Hours with a Geometric Group Theorist

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691158662
- eISBN:
- 9781400885398
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691158662.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the automorphisms of free groups. Every group is the collection of symmetries of some object, namely, its Cayley graph. A symmetry of a group is called an automorphism; it is ... More

## Strictly Semi-linear Automorphisms

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0030
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the action of a strictly semi-linear automorphism fixing a root on the corresponding root group. It begins with the hypothesis whereby Δ is a Moufang spherical building and Π ... More

## Constructing Simple Structures

*Byunghan Kim*

### in Simplicity Theory

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198567387
- eISBN:
- 9780191746512
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567387.003.0006
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

In this chapter, several methods of constructing simple structures,including the Hrushovski construction, are introduced.These methods are used in finding a counterexample, or producing a canonical ... More

## Coxeter Groups

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0019
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter develops a theory of descent for buildings by assembling various results about Coxeter groups. It begins with the notation stating that W is an arbitrary group with a distinguished set ... More

## Linear Automorphisms

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0029
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the notion of a linear automorphism of an arbitrary spherical building satisfying the Moufang property. It begins with the notation whereby Ω = (U₊, U₁, ..., Uₙ) is the root ... More