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## CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES

*Hajime Ishihara*

### in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0016
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes a base formal system for constructive reverse mathematics to classify various theorems in intuitionistic, constructive recursive, and classical mathematics by logical ... More

## Reverse Mathematics: Proofs from the Inside Out

*John Stillwell*

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691196411
- eISBN:
- 9781400889037
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691196411.001.0001
- Subject:
- Mathematics, History of Mathematics

Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have ... More

## A Bigger Picture

*John Stillwell*

### in Reverse Mathematics: Proofs from the Inside Out

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691196411
- eISBN:
- 9781400889037
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691196411.003.0008
- Subject:
- Mathematics, History of Mathematics

This chapter aims to pick up some of the ideas dropped from this book and set them in a bigger picture of logic and computability theory. It begins with a sketch of constructive mathematics. ... More

## Historical Introduction

*John Stillwell*

### in Reverse Mathematics: Proofs from the Inside Out

- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691196411
- eISBN:
- 9781400889037
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691196411.003.0001
- Subject:
- Mathematics, History of Mathematics

This chapter prepares the reader's mind for reverse mathematics. As its name suggests, reverse mathematics seeks not theorems but the right axioms to prove theorems already known. Reverse mathematics ... More

## Statistical Inference via Convex Optimization: Proofs from the Inside Out

*John Stillwell*

- Published in print:
- 2019
- Published Online:
- September 2020
- ISBN:
- 9780691197296
- eISBN:
- 9780691200316
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691197296.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization

Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have ... More

##
Sparse Recovery via *ℓ*_{1} Minimization

*John Stillwell*

### in Statistical Inference via Convex Optimization: Proofs from the Inside Out

- Published in print:
- 2019
- Published Online:
- September 2020
- ISBN:
- 9780691197296
- eISBN:
- 9780691200316
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691197296.003.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter prepares the reader's mind for reverse mathematics. As its name suggests, reverse mathematics seeks not theorems but the right axioms to prove theorems already known. Reverse mathematics ... More

## Hypothesis Testing

*John Stillwell*

### in Statistical Inference via Convex Optimization: Proofs from the Inside Out

- Published in print:
- 2019
- Published Online:
- September 2020
- ISBN:
- 9780691197296
- eISBN:
- 9780691200316
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691197296.003.0002
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter prepares the reader's mind for reverse mathematics. As its name suggests, reverse mathematics seeks not theorems but the right axioms to prove theorems already known. Reverse mathematics ... More

## From Hypothesis Testing to Estimating Functionals

*John Stillwell*

### in Statistical Inference via Convex Optimization: Proofs from the Inside Out

- Published in print:
- 2019
- Published Online:
- September 2020
- ISBN:
- 9780691197296
- eISBN:
- 9780691200316
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691197296.003.0003
- Subject:
- Mathematics, Computational Mathematics / Optimization

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