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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


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