## Keys to First Corinthians: Revisiting the Major Issues

*Jerome Murphy-O'Connor*

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199564156
- eISBN:
- 9780191721281
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564156.001.0001
- Subject:
- Religion, Biblical Studies

This book brings together sixteen originally independent articles dealing with various aspects of 1 Corinthians and published between 1976 and 1993. As the series develops there are more frequent ... More

## THE INTERPOLATION THEOREM IN INTUITIONISTIC PREDICATE CALCULUS

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0004
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents the equivalence of Craig's interpolation property to Robinson's joint consistency, and a proof of Lyndon's interpolation theorem for the classical predicate logic. It is proved ... More

## INTERPOLATION AND DEFINABILITY IN QUANTIFIED LOGICS

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a proof of Lyndon's interpolation property (LIP) for quantified extensions of basic modal logics K, T, D, K4, and S4, and for some others, including the propositional S5 has ... More

## INTERPOLATION IN NORMAL EXTENSIONS OF THE MODAL LOGIC S4

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0008
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

It appears that the behaviour of interpolation over the modal S4 logic is similar to interpolation in superintuitionistic logics. It is shown that all extensions of S4 with interpolation property for ... More

## Spatial variation in risk

*Dirk U. Pfeiffer, Timothy P. Robinson, Mark Stevenson, Kim B. Stevens, David J. Rogers, and Archie C. A. Clements*

### in Spatial Analysis in Epidemiology

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198509882
- eISBN:
- 9780191709128
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509882.003.0006
- Subject:
- Biology, Disease Ecology / Epidemiology

This chapter discusses spatial variation in risk. Epidemiological disease investigations should include an assessment of the spatial variation of disease risk, as this may provide important clues ... More

## Commentary

*H. A. G. Houghton*

### in Augustine's Text of John: Patristic Citations and Latin Gospel Manuscripts

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199545926
- eISBN:
- 9780191719974
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199545926.003.0013
- Subject:
- Religion, Early Christian Studies

The textual commentary treats Augustine's text of John verse by verse, concentrating on variants from the Vulgate. There are a number of occasions on which Augustine has a reading not attested in ... 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

## CRAIG'S THEOREM IN SUPERINTUITIONISTIC LOGICS AND AMALGAMABLE VARIETIES OF PSEUDOBOOLEAN ALGEBRAS

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0006
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a full description of superintuitionistic logics with Craig's interpolation property CIP. It turns out that in the continuum of intermediate logics, only seven have Craig's ... More

## ALTERNATIVE APPROACHES

*D. A. Bini, G. Latouche, and B. Meini*

### in Numerical Methods for Structured Markov Chains

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198527688
- eISBN:
- 9780191713286
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527688.003.0008
- Subject:
- Mathematics, Numerical Analysis

Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of ... More

## INTERPOLATION IN MODAL INFINITE SLICE LOGICS CONTAINING THE LOGIC K4

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter examines the family NE(K) of normal extensions of K4. With any such logic L its reflexive fragment r(L) is associated, which contains the logic S4. A logic L is of infinite slice if ... More

## SYNTACTIC PROOF OF INTERPOLATION FOR THE INTUITIONISTIC PREDICATE LOGIC

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0013
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents a syntactic proof of the Lyndon interpolation theorem for the intuitionistic predicate logic. It is a modification of a proof of the interpolation theorem found by K. Schütte, ... More

## INTERPOLATION BY TRANSLATION

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0014
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes some uniform algorithmic methodology for finding interpolants in various logic. It operates with translations of non-classical logics into classical first-order theories and ... More

## INTERPOLATION IN (INTUITIONISTIC) LOGIC PROGRAMMING

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0015
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides interpolation results for the Horn clause fragment of classical or intuitionistic logic. A weak variant of interpolation for a fragment of the intuitionistic predicate logic ... More

## INTERPOLATION IN GOAL- DIRECTED PROOF SYSTEMS

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0016
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies the interpolation properties for implicational fragment of a variety of substructural, strict modal, and intuitionistic and intermediate logics. The methodology is ... More

## FURTHER RESULTS AND DISCUSSION

*D.M. Gabbay and L. Maksimova*

### in Interpolation and Definability: Modal and Intuitionistic Logics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198511748
- eISBN:
- 9780191705779
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198511748.003.0017
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses further directions of research. A brief review of the results obtained on interpolation and definability, which were not included in this volume, is presented.

## Interpolations in 1 Corinthians

*Jerome Murphy‐O'Connor*

### in Keys to First Corinthians: Revisiting the Major Issues

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199564156
- eISBN:
- 9780191721281
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564156.003.00016
- Subject:
- Religion, Biblical Studies

After a discussion of the validity of the methodology normally used to determine interpolations, i.e. additions to a text after it had left its author's hands, the chapter passes in review thirteen ... More

## Finite Elements on Tetrahedra

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0005
- Subject:
- Mathematics, Numerical Analysis

The finite element method is based on a geometric decomposition of the domain of Maxwell’s equations into simple elements. This chapter is devoted to tetrahedral elements, which are very common in ... More

## Finite Elements on Hexahedra

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0006
- Subject:
- Mathematics, Numerical Analysis

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several ... More

## THE MATHEMATICAL SETTING

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0003
- Subject:
- Mathematics, Applied Mathematics

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as ... More

## DISCRETE SYSTEMS AND FREE-DISCONTINUITY PROBLEMS

*Andrea Braides*

### in Gamma-Convergence for Beginners

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0012
- Subject:
- Mathematics, Applied Mathematics

This chapter shows how general non-convex difference schemes can give rise to functionals defined by piecewise-Sobolev functions with interactions between surface and volume terms. Different ... More