The Birth of Model Theory : : Löwenheim's Theorem in the Frame of the Theory of Relatives / / Calixto Badesa.
Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant the...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2004 |
Year of Publication: | 2009 |
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Badesa, Calixto, author. aut http://id.loc.gov/vocabulary/relators/aut The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / Calixto Badesa. Course Book Princeton, NJ : Princeton University Press, [2009] ©2004 1 online resource (256 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- Chapter 1. Algebra of Classes and Propositional Calculus -- Chapter 2. The Theory of Relatives -- Chapter 3. Changing the Order of Quantifiers -- Chapter 4. The Löwenheim Normal Form -- Chapter 5. Preliminaries to Löwenheim's Theorem -- Chapter 6. Löwenheim's Theorem -- Appendix. First-Order Logic with Fleeing Indices -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible. Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics. 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 30. Aug 2021) L'owenheim, Leopold. Logic, Symbolic and mathematical. Model theory. MATHEMATICS / Logic. bisacsh Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691058535 https://doi.org/10.1515/9781400826186 https://www.degruyter.com/isbn/9781400826186 Cover https://www.degruyter.com/cover/covers/9781400826186.jpg |
language |
English |
format |
eBook |
author |
Badesa, Calixto, Badesa, Calixto, |
spellingShingle |
Badesa, Calixto, Badesa, Calixto, The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / Frontmatter -- Contents -- Preface -- Chapter 1. Algebra of Classes and Propositional Calculus -- Chapter 2. The Theory of Relatives -- Chapter 3. Changing the Order of Quantifiers -- Chapter 4. The Löwenheim Normal Form -- Chapter 5. Preliminaries to Löwenheim's Theorem -- Chapter 6. Löwenheim's Theorem -- Appendix. First-Order Logic with Fleeing Indices -- References -- Index |
author_facet |
Badesa, Calixto, Badesa, Calixto, |
author_variant |
c b cb c b cb |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Badesa, Calixto, |
title |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / |
title_sub |
Löwenheim's Theorem in the Frame of the Theory of Relatives / |
title_full |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / Calixto Badesa. |
title_fullStr |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / Calixto Badesa. |
title_full_unstemmed |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / Calixto Badesa. |
title_auth |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter 1. Algebra of Classes and Propositional Calculus -- Chapter 2. The Theory of Relatives -- Chapter 3. Changing the Order of Quantifiers -- Chapter 4. The Löwenheim Normal Form -- Chapter 5. Preliminaries to Löwenheim's Theorem -- Chapter 6. Löwenheim's Theorem -- Appendix. First-Order Logic with Fleeing Indices -- References -- Index |
title_new |
The Birth of Model Theory : |
title_sort |
the birth of model theory : löwenheim's theorem in the frame of the theory of relatives / |
publisher |
Princeton University Press, |
publishDate |
2009 |
physical |
1 online resource (256 p.) Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Chapter 1. Algebra of Classes and Propositional Calculus -- Chapter 2. The Theory of Relatives -- Chapter 3. Changing the Order of Quantifiers -- Chapter 4. The Löwenheim Normal Form -- Chapter 5. Preliminaries to Löwenheim's Theorem -- Chapter 6. Löwenheim's Theorem -- Appendix. First-Order Logic with Fleeing Indices -- References -- Index |
isbn |
9781400826186 9783110442502 9780691058535 |
url |
https://doi.org/10.1515/9781400826186 https://www.degruyter.com/isbn/9781400826186 https://www.degruyter.com/cover/covers/9781400826186.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511.3092 |
dewey-sort |
3511.3092 |
dewey-raw |
511.3092 |
dewey-search |
511.3092 |
doi_str_mv |
10.1515/9781400826186 |
oclc_num |
1004871999 |
work_keys_str_mv |
AT badesacalixto thebirthofmodeltheorylowenheimstheoremintheframeofthetheoryofrelatives AT badesacalixto birthofmodeltheorylowenheimstheoremintheframeofthetheoryofrelatives |
status_str |
n |
ids_txt_mv |
(DE-B1597)446449 (OCoLC)1004871999 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
The Birth of Model Theory : Löwenheim's Theorem in the Frame of the Theory of Relatives / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
_version_ |
1770176642074804224 |
fullrecord |
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