## SOLUBLE GROUPS OF FINITE RANK

*John C. Lennox and Derek J. S. Robinson*

### in The Theory of Infinite Soluble Groups

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0005
- Subject:
- Mathematics, Pure Mathematics

This chapter details the ranks of an abelian group. It also talks about the structure of soluble groups with finite rank, minimax groups, and residual finiteness.

## THE THEORY OF FINITELY GENERATED SOLUBLE GROUPS II

*John C. Lennox and Derek J. S. Robinson*

### in The Theory of Infinite Soluble Groups

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0007
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, the Artin-Rees property, and residual finiteness. It also talks about the Frattini subgroup.

## Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics

*Colin McLarty*

*Apostolos Doxiadis and Barry Mazur (eds)*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0004
- Subject:
- Mathematics, History of Mathematics

This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In ... More

## Truth and Meaning

*Donald Davidson*

### in Inquiries into Truth and Interpretation

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0002
- Subject:
- Philosophy, Philosophy of Language

Develops the criterion of learnability proposed in Essay 1 into a constraint for a satisfactory theory of meaning: such a theory must show how, on the basis of a finite stock of semantic primitives, ... More

## Semantics for Natural Languages

*Donald Davidson*

### in Inquiries into Truth and Interpretation

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0004
- Subject:
- Philosophy, Philosophy of Language

Davidson rehearses the demands for an acceptable theory of meaning for a natural language—that it give the meaning for each (actual and potential) utterance in the language, that it do so by finite ... More

## Infinity and the Past

*Quentin Smith*

### in Theism, Atheism, and Big Bang Cosmology

- Published in print:
- 1995
- Published Online:
- October 2011
- ISBN:
- 9780198263838
- eISBN:
- 9780191682650
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198263838.003.0002
- Subject:
- Religion, Philosophy of Religion, Theology

This chapter presents an essay which aims to refute the argument that the past is necessarily finite. It considers the arguments offered by William Lane Craig and arguments by other philosophers. It ... More

## Subordination

*Sonia Cristofaro*

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780199282005
- eISBN:
- 9780191719271
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199282005.001.0001
- Subject:
- Linguistics, Syntax and Morphology

This book presents a typology of subordination systems across the world's languages. Traditional definitions of subordination are based on morphosyntactic criteria, such as clausal embedding or ... More

## Theories of Meaning and Learnable Languages

*Donald Davidson*

### in Inquiries into Truth and Interpretation

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0001
- Subject:
- Philosophy, Philosophy of Language

Davidson asks what properties a language must have to be learnable. He criticizes a (then) popular response that models the order of language acquisition on the epistemological priority of the types ... More

## Some Thoughts on Radical Indeterminacy

*Hartry Field*

### in Truth and the Absence of Fact

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0009
- Subject:
- Philosophy, General

Discusses some issues about indeterminacy of reference and truth, from two points of view about reference and truth: that of a correspondence theory and that of a disquotational theory. It is argued ... More

## Mathematical Objectivity and Mathematical Objects

*Hartry Field*

### in Truth and the Absence of Fact

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0011
- Subject:
- Philosophy, General

Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the ... More

## Which Undecidable Mathematical Sentences Have Determinate Truth Values?

*Hartry Field*

### in Truth and the Absence of Fact

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0012
- Subject:
- Philosophy, General

Argues that typical undecidable sentences of set theory (e.g. about the size of the continuum) can have no determinate truth‐value, since nothing in our practice can determine which ‘universe of ... More

## The Substance of Language Volume I: The Domain of Syntax

*John M. Anderson*

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.001.0001
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology

This book explores the consequences for syntax of assuming that language is substantively based, or grounded, in extralinguistic cognition and perception. Groundedness does not just apply to the ... More

## Interrogatives

*John M. Anderson*

### in The Substance of Language Volume I: The Domain of Syntax

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.003.0005
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology

Interrogative is a mood, a secondary category of the functional category of finiteness. Different kinds of interrogative structure are described in terms of the framework of Chapter 3. These include ... More

## Finiteness and mood

*John M. Anderson*

### in The Substance of Language Volume I: The Domain of Syntax

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.003.0007
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology

Finiteness is interpreted here as the category licensing potential independence of a predication, and mood is a secondary category that grammaticalizes speech‐act type. As such it is limited to ... More

## Canonical Morphology and Syntax

*Dunstan Brown, Marina Chumakina, and Greville G. Corbett (eds)*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199604326
- eISBN:
- 9780191746154
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199604326.001.0001
- Subject:
- Linguistics, Syntax and Morphology, Theoretical Linguistics

This is the first book to present Canonical Typology, a framework for comparing constructions and categories across languages. The canonical method takes the criteria used to define particular ... More

## Unpacking finiteness

*Irina Nikolaeva*

### in Canonical Morphology and Syntax

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199604326
- eISBN:
- 9780191746154
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199604326.003.0005
- Subject:
- Linguistics, Syntax and Morphology, Theoretical Linguistics

Since no implicational relations suggested for finiteness parameters so far have been without exceptions, it is argued that finiteness is a clausal notion which is best characterized by independent ... More

## Homotopy Groups and CW Complexes

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0002
- Subject:
- Mathematics, Educational Mathematics

This chapter discusses some results about homotopy groups and CW complexes. Throughout this book, one needs to assume a certain amount of algebraic topology. A CW complex is a topological space built ... More

## Free Groups and Folding

*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/9780691158662.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show ... More

## Entropy for hyperbolic Riemann surface laminations I

*Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony*

*Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)*

### in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0020
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of ... More

## Entropy for hyperbolic Riemann surface laminations II

*Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony*

*Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)*

### in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0021
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated ... More