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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 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

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


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