Predicative Arithmetic. (MN-32) /

Predicative Arithmetic. (MN-32) / / Edward Nelson.

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed...

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Superior document:Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999
VerfasserIn:
Nelson, Edward,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2014]
©1986
Year of Publication:2014
Edition:Course Book
Language:English
Series:Mathematical Notes ; 32
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Physical Description:1 online resource (200 p.)
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(OCoLC)979686371
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Predicative Arithmetic. (MN-32) / Edward Nelson.
Course Book
Princeton, NJ : Princeton University Press, [2014]
©1986
1 online resource (200 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Mathematical Notes ; 32
Frontmatter -- Acknowledgments -- Table of Contents -- Chapter 1. The impredicativity of induction -- Chapter 2. Logical terminology -- Chapter 3. The axioms of arithmetic -- Chapter 4. Order -- Chapter 5. Induction by relativization -- Chapter 6. Interpretability in Robinson's theory -- Chapter 7. Bounded induction -- Chapter 8. The bounded least number principle -- Chapter 9. The euclidean algorithm -- Chapter 10. Encoding -- Chapter 11. Bounded separation and minimum -- Chapter 12. Sets and functions -- Chapter 13. Exponential functions -- Chapter 14. Exponentiation -- Chapter 15. A stronger relativization scheme -- Chapter 16. Bounds on exponential functions -- Chapter 17. Bounded replacement -- Chapter 18. An impassable barrier -- Chapter 19. Sequences -- Chapter 20. Cardinality -- Chapter 21. Existence of sets -- Chapter 22. Semibounded Replacement -- Chapter 23. Formulas -- Chapter 24. Proofs -- Chapter 25. Derived rules of inference -- Chapter 26. Special constants -- Chapter 27. Extensions by definition -- Chapter 28. Interpretations -- Chapter 29. The arithmetization of arithmetic -- Chapter 30. The consistency theorem -- Chapter 31. Is exponentiation total? -- Chapter 32. A modified Hilbert program -- Bibliography -- General index -- Index of defining axioms
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Arithmetic.
Constructive mathematics.
MATHEMATICS / Arithmetic. bisacsh
Addition.
Adjunction (field theory).
Age of the universe.
Almost surely.
Arithmetic IF.
Atomic formula.
Axiom.
Axiomatic system.
Beta function.
Big O notation.
Binary number.
Binary relation.
Brownian motion.
Canonical form.
Cardinality.
Cartesian coordinate system.
Chessboard.
Classical mathematics.
Closed-form expression.
Commutative property.
Computation.
Conservative extension.
Consistency.
Contradiction.
Deduction theorem.
Diameter.
Direct proof.
Domain of discourse.
Elementary mathematics.
Elias M. Stein.
Existential quantification.
Exponential function.
Exponentiation.
Extension by definitions.
Finitary.
Finite set.
Formula C (SCCA).
Foundations of mathematics.
Fundamenta Mathematicae.
Gödel's completeness theorem.
Herbrand's theorem.
Impredicativity.
Inaccessible cardinal.
Inference.
Interpretability.
John Milnor.
Logic.
Logical connective.
Mathematical induction.
Mathematical logic.
Mathematician.
Mathematics.
Measurable cardinal.
Metamathematics.
Metatheorem.
Model theory.
Mostowski.
Natural number.
Negation.
Non-standard analysis.
Notation.
P-adic analysis.
Peano axioms.
Polynomial.
Positional notation.
Power of two.
Power set.
Primitive notion.
Primitive recursive function.
Principia Mathematica.
Probability theory.
Quantifier (logic).
Quantity.
Ranking (information retrieval).
Rational number.
Real number.
Recursion (computer science).
Remainder.
Requirement.
Robert Langlands.
Rule of inference.
Scientific notation.
Sequence.
Set theory.
Subset.
Theorem.
Theory.
Transfer principle.
Transfinite number.
Triviality (mathematics).
Tuple.
Uniqueness.
Universal quantification.
Variable (mathematics).
Zermelo-Fraenkel set theory.
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999 9783110413441
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science 9783110413595
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691610290
https://doi.org/10.1515/9781400858927
https://www.degruyter.com/isbn/9781400858927
Cover https://www.degruyter.com/document/cover/isbn/9781400858927/original
language English
format eBook
author Nelson, Edward,
Nelson, Edward,
spellingShingle Nelson, Edward,
Nelson, Edward,
Predicative Arithmetic. (MN-32) /
Mathematical Notes ;
Frontmatter --
Acknowledgments --
Table of Contents --
Chapter 1. The impredicativity of induction --
Chapter 2. Logical terminology --
Chapter 3. The axioms of arithmetic --
Chapter 4. Order --
Chapter 5. Induction by relativization --
Chapter 6. Interpretability in Robinson's theory --
Chapter 7. Bounded induction --
Chapter 8. The bounded least number principle --
Chapter 9. The euclidean algorithm --
Chapter 10. Encoding --
Chapter 11. Bounded separation and minimum --
Chapter 12. Sets and functions --
Chapter 13. Exponential functions --
Chapter 14. Exponentiation --
Chapter 15. A stronger relativization scheme --
Chapter 16. Bounds on exponential functions --
Chapter 17. Bounded replacement --
Chapter 18. An impassable barrier --
Chapter 19. Sequences --
Chapter 20. Cardinality --
Chapter 21. Existence of sets --
Chapter 22. Semibounded Replacement --
Chapter 23. Formulas --
Chapter 24. Proofs --
Chapter 25. Derived rules of inference --
Chapter 26. Special constants --
Chapter 27. Extensions by definition --
Chapter 28. Interpretations --
Chapter 29. The arithmetization of arithmetic --
Chapter 30. The consistency theorem --
Chapter 31. Is exponentiation total? --
Chapter 32. A modified Hilbert program --
Bibliography --
General index --
Index of defining axioms
author_facet Nelson, Edward,
Nelson, Edward,
author_variant e n en
e n en
author_role VerfasserIn
VerfasserIn
author_sort Nelson, Edward,
title Predicative Arithmetic. (MN-32) /
title_full Predicative Arithmetic. (MN-32) / Edward Nelson.
title_fullStr Predicative Arithmetic. (MN-32) / Edward Nelson.
title_full_unstemmed Predicative Arithmetic. (MN-32) / Edward Nelson.
title_auth Predicative Arithmetic. (MN-32) /
title_alt Frontmatter --
Acknowledgments --
Table of Contents --
Chapter 1. The impredicativity of induction --
Chapter 2. Logical terminology --
Chapter 3. The axioms of arithmetic --
Chapter 4. Order --
Chapter 5. Induction by relativization --
Chapter 6. Interpretability in Robinson's theory --
Chapter 7. Bounded induction --
Chapter 8. The bounded least number principle --
Chapter 9. The euclidean algorithm --
Chapter 10. Encoding --
Chapter 11. Bounded separation and minimum --
Chapter 12. Sets and functions --
Chapter 13. Exponential functions --
Chapter 14. Exponentiation --
Chapter 15. A stronger relativization scheme --
Chapter 16. Bounds on exponential functions --
Chapter 17. Bounded replacement --
Chapter 18. An impassable barrier --
Chapter 19. Sequences --
Chapter 20. Cardinality --
Chapter 21. Existence of sets --
Chapter 22. Semibounded Replacement --
Chapter 23. Formulas --
Chapter 24. Proofs --
Chapter 25. Derived rules of inference --
Chapter 26. Special constants --
Chapter 27. Extensions by definition --
Chapter 28. Interpretations --
Chapter 29. The arithmetization of arithmetic --
Chapter 30. The consistency theorem --
Chapter 31. Is exponentiation total? --
Chapter 32. A modified Hilbert program --
Bibliography --
General index --
Index of defining axioms
title_new Predicative Arithmetic. (MN-32) /
title_sort predicative arithmetic. (mn-32) /
series Mathematical Notes ;
series2 Mathematical Notes ;
publisher Princeton University Press,
publishDate 2014
physical 1 online resource (200 p.)
Issued also in print.
edition Course Book
contents Frontmatter --
Acknowledgments --
Table of Contents --
Chapter 1. The impredicativity of induction --
Chapter 2. Logical terminology --
Chapter 3. The axioms of arithmetic --
Chapter 4. Order --
Chapter 5. Induction by relativization --
Chapter 6. Interpretability in Robinson's theory --
Chapter 7. Bounded induction --
Chapter 8. The bounded least number principle --
Chapter 9. The euclidean algorithm --
Chapter 10. Encoding --
Chapter 11. Bounded separation and minimum --
Chapter 12. Sets and functions --
Chapter 13. Exponential functions --
Chapter 14. Exponentiation --
Chapter 15. A stronger relativization scheme --
Chapter 16. Bounds on exponential functions --
Chapter 17. Bounded replacement --
Chapter 18. An impassable barrier --
Chapter 19. Sequences --
Chapter 20. Cardinality --
Chapter 21. Existence of sets --
Chapter 22. Semibounded Replacement --
Chapter 23. Formulas --
Chapter 24. Proofs --
Chapter 25. Derived rules of inference --
Chapter 26. Special constants --
Chapter 27. Extensions by definition --
Chapter 28. Interpretations --
Chapter 29. The arithmetization of arithmetic --
Chapter 30. The consistency theorem --
Chapter 31. Is exponentiation total? --
Chapter 32. A modified Hilbert program --
Bibliography --
General index --
Index of defining axioms
isbn 9781400858927
9783110413441
9783110413595
9783110494921
9783110665925
9783110442496
9780691610290
callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA9
callnumber-sort QA 19.56
url https://doi.org/10.1515/9781400858927
https://www.degruyter.com/isbn/9781400858927
https://www.degruyter.com/document/cover/isbn/9781400858927/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 511 - General principles of mathematics
dewey-full 511.3
dewey-sort 3511.3
dewey-raw 511.3
dewey-search 511.3
doi_str_mv 10.1515/9781400858927
oclc_num 979686371
work_keys_str_mv AT nelsonedward predicativearithmeticmn32
status_str n
ids_txt_mv (DE-B1597)448213
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carrierType_str_mv cr
hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Predicative Arithmetic. (MN-32) /
container_title Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999
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