The Birth of Model Theory: Löwenheim's Theorem in the Frame of the Theory of RelativesLöwenheim'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. |
Contents
1 | |
Chapter 2 The Theory of Relatives | 31 |
Chapter 3 Changing the Order of Quantifiers | 73 |
Chapter 4 The Löwenheim Normal Form | 107 |
Chapter 5 Preliminaries to Löwenheims Theorem | 129 |
Chapter 6 Löwenheims Theorem | 143 |
Appendix FirstOrder Logic with Fleeing Indices | 207 |
227 | |
237 | |
Other editions - View all
The Birth of Model Theory: Lowenheim's Theorem in the Frame of the Theory of ... Calixto Badesa No preview available - 2004 |