Author | Beeson, Michael J. author |
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Title | Foundations of Constructive Mathematics [electronic resource] : Metamathematical Studies / by Michael J. Beeson |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1985 |
Connect to | http://dx.doi.org/10.1007/978-3-642-68952-9 |
Descript | XXIII, 466 p. online resource |
One. Practice and Philosophy of Constructive Mathematics -- I. Examples of Constructive Mathematics -- II. Informal Foundations of Constructive Mathematics -- III. Some Different Philosophies of Constructive Mathematics -- IV. Recursive Mathematics: Living with Churchโs Thesis -- V. The Role of Formal Systems in Foundational Studies -- Two. Formal Systems of the Seventies -- VI. Theories of Rules -- VII. Readability -- VIII. Constructive Set Theories -- IX. The Existence Property in Constructive Set Theory -- X. Theories of Rules, Sets, and Classes -- XI. Constructive Type Theories -- Three. Metamathematical Studies -- XII. Constructive Models of Set Theory -- XIII. Proof-Theoretic Strength -- XIV. Some Formalized Metamathematics and Churchโs Rule -- XV. Forcing -- XVI. Continuity -- Four. Metaphilosophical Studies -- XVII. Theories of Rules and Proofs -- Historical Appendix -- 1. From Gauss to Zermelo: The Origins of Non-Constructive Mathematics -- 2. From Kant to Hilbert: Logic and Philosophy -- 3. Brouwer and the Dutch Intuitionists -- 4. Early Formal Systems for Intuitionism -- 5. Kleene: The Marriage of Recursion Theory and Intuitionism -- 6. The Russian Constructivists and Recursive Analysis -- 7. Model Theory of Intuitionistic Systems -- 8. Logical Studies of Intuitionistic Systems -- 9. Bishop and his Followers -- 10. The Latest Decade -- References -- Index of Axioms, Abbreviations, and Theories -- Index of Names -- Index of Symbols