Subsystems of Second Order Arithmetic

Klappentext Through a series of case studies! this volume examines these axioms to prove particular theorems in core mathematical areas. Zusammenfassung What are the appropriate axioms for mathematics? Through a series of case studies! this volume examines these axioms to prove particular theorems in core areas including algebra! analysis! and topology! focusing on the language of second-order arithmetic! the weakest language rich enough to express and develop the bulk of mathematics. Inhaltsverzeichnis List of tables; Preface; Acknowledgements; 1. Introduction; Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension; 3. Arithmetical comprehension; 4. Weak König's lemma; 5. Arithmetical transfinite recursion; 6. 11 comprehension; Part II. Models of Subsystems of Z2: 7. ß-models; 8. -models; 9. Non- -models; Part III. Appendix: 10. Additional results; Bibliography; Index.

Klappentext
An original contribution to the foundations of mathematics, with emphasis on the role of set existence axioms, this book gives particular attention to several well known foundational programs including those by Hilbert, Bishop, and Weyl.

Zusammenfassung
What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics.

Inhalt
List of tables; Preface; Acknowledgements; 1. Introduction; Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension; 3. Arithmetical comprehension; 4. Weak König's lemma; 5. Arithmetical transfinite recursion; 6. 11 comprehension; Part II. Models of Subsystems of Z2: 7. ß-models; 8. -models; 9. Non- -models; Part III. Appendix: 10. Additional results; Bibliography; Index.

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