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## Lowness properties and K-triviality

*André Nies*

### in Computability and Randomness

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199230761
- eISBN:
- 9780191710988
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230761.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter shows the equivalence of K-triviality and lowness for Martin–Löf randomness. This coincidence extends to other lowness properties, such as being a base for Martin–Löf randomness, and ... More

## Martin-Löf randomness and its variants

*André Nies*

### in Computability and Randomness

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199230761
- eISBN:
- 9780191710988
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230761.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter begins with a general background on how to introduce mathematical randomness notions. It then studies the central randomness notion of Martin–Löf, and gives some connections to ... More

## Randomness and betting strategies

*André Nies*

### in Computability and Randomness

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199230761
- eISBN:
- 9780191710988
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230761.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Martingales form the mathematical counterpart of betting strategies. This chapter studies computable randomness, where the tests are computable martingales, and separates it from both Martin–Löf ... More

## The Modern Theory of Induction

*Kumaraswamy Velupillai*

### in Computable Economics: The Arne Ryde Memorial Lectures

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198295273
- eISBN:
- 9780191596988
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198295278.003.0005
- Subject:
- Economics and Finance, Macro- and Monetary Economics

A theory of induction, based on the formalism of algorithmic complexity theory, is introduced in this chapter. This is then used to underpin a theory of learning and a computable basis for inductive ... More

## Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

*David Corfield*

- Published in print:
- 2020
- Published Online:
- March 2020
- ISBN:
- 9780198853404
- eISBN:
- 9780191888069
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853404.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

In[KF1] 1914, in an essay entitled ‘Logic as the Essence of Philosophy’, Bertrand Russell promised to revolutionize philosophy by introducing there the ‘new logic’ of Frege and Peano: “The old logic ... More

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