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## AN ANALOGUE OF BETH'S THEOREM IN NORMAL EXTENSIONS OF THE MODAL 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/9780198511748.003.0011
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Beth's theorems state that in the classical predicate logic, any implicitly definable predicate is explicitly definable. This chapter proves an analogue of this theorem for all extensions of K4. It ... 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

## Opening Questions, Following Rules

*Paul Bloomfield*

### in Metaethics after Moore

- Published in print:
- 2006
- Published Online:
- May 2010
- ISBN:
- 9780199269914
- eISBN:
- 9780191710032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269914.003.0009
- Subject:
- Philosophy, Moral Philosophy, General

This chapter begins by noting that the 20th century beneficiary of the open question argument has been (rather ironically) the class of non-realist views, including non-cognitivism and expressivism. ... More

## Inessential features and expressive power of descriptive metalanguages

*Geoffrey K. Pullum and Hans‐Jörg Tiede*

### in Features: Perspectives on a Key Notion in Linguistics

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199577743
- eISBN:
- 9780191722844
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577743.003.0011
- Subject:
- Linguistics, Semantics and Pragmatics, Syntax and Morphology

Linguists feel intuitively that genuine features, those reflecting properties of natural language, are distinguishable from spurious ones – mere tricks exploiting feature machinery. Unfortunately, no ... More

## Truth and Merit

*Charles Travis*

### in Objectivity and the Parochial

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199596218
- eISBN:
- 9780191595783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199596218.003.0009
- Subject:
- Philosophy, Aesthetics

This chapter compares Frege and Austin on truth. One might think that these thinkers held opposing views on truth. But, at least for the most part, there is no reason to think this. It is better, it ... More

## Formalization: Expressibility, Definability, Compositionality

*Stanley Peters*

### in Quantifiers in Language and Logic

- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780199291267
- eISBN:
- 9780191700590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199291267.003.0013
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter discusses logical equivalence across languages in terms of the concept of a lexical mapping and addresses the issue of compositionality. Compositionality is perhaps the first extra ... More

## Definability and Undefinability in Logical Languages: Tools for the Monadic Case

*Stanley Peters*

### in Quantifiers in Language and Logic

- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780199291267
- eISBN:
- 9780191700590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199291267.003.0014
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

To prove a positive definability result, one usually has to exhibit the defining sentence, and it helps if this sentence belongs to a well-defined language. To prove a negative undefinability result, ... More

## Applications to Monadic Definability

*Stanley Peters*

### in Quantifiers in Language and Logic

- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780199291267
- eISBN:
- 9780191700590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199291267.003.0015
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter applies the Ehrenfeucht-Fraïssé (EF) technique to present a variety of results about the expressive power of certain monadic quantifiers. After repeating the general method, ... More

## Advanced Metatheory

*Stewart Shapiro*

### in Foundations without Foundationalism: A Case for Second-Order Logic

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250296
- eISBN:
- 9780191598388
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250290.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

After setting out some issues concerning the meta‐language, this chapter presents a number of results about second‐order languages with standard semantics. Since the membership relation can be ... More

## Curves

*Ehud Hrushovski and François Loeser*

### in Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691161686
- eISBN:
- 9781400881222
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161686.003.0007
- Subject:
- Mathematics, Geometry / Topology

This chapter proves the iso-definability of unit vector C when C is a curve using Riemann-Roch. Recall that a pro-definable set is called iso-definable if it is isomorphic, as a pro-definable set, to ... More

## Theories of presheaf type: general criteria

*Olivia Caramello*

### in Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

- Published in print:
- 2017
- Published Online:
- March 2018
- ISBN:
- 9780198758914
- eISBN:
- 9780191818752
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198758914.003.0008
- Subject:
- Mathematics, Geometry / Topology, Pure Mathematics

This chapter carries out a systematic investigation of the class of geometric theories of presheaf type (i.e. classified by a presheaf topos), by using in particular the results on flat functors ... More

## Paradoxes of Definability, Russell’s Paradox, the Liar

*Keith Simmons*

### in Semantic Singularities: Paradoxes of Reference, Predication, and Truth

- Published in print:
- 2018
- Published Online:
- July 2018
- ISBN:
- 9780198791546
- eISBN:
- 9780191852923
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791546.003.0005
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Chapter 5 moves beyond the simple paradoxes discussed in Chapters 2-4. The chapter applies the singularity approach to the traditional paradoxes of definability (or denotation), associated with ... More

## Wilfrid Hodges A short history of model theory

*Tim Button and Sean Walsh*

### in Philosophy and Model Theory

- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198790396
- eISBN:
- 9780191863424
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198790396.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

We give a historical account of mathematical model theory, from its origins to the early twenty-first century. We record how early work in model theory grew from attempts to formalise and systematise ... More

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