Cover -- Half-title -- Series information -- Title page -- Copyright information -- Table of contents -- Preface -- Part I Invited Papers -- Gödel's program for new axioms: Why, where, how and what? -- 1. Why new axioms? -- 2. Where should one look for new axioms? -- 3. How is the unfolding of a system defined? -- 4. The expansive closure of non-flnitist arithmetic: what's obtained -- 5. The unfolding of set theory -- References -- Infinite-valued Gödel Logics with 0-1-Projections and Relativizations* -- 1. Introduction -- 2. Propositional Gödel logics -- 3. Completeness of propositional Gödel logics with projections -- 4. First-order Gödel logics -- 5. Incompleteness of first-order Gödel logics with 0-1-projections and relativizations -- 6. Conclusion -- References -- Contributions of K. Gödel to Relativity and Cosmology* -- 1. Introduction -- 2. Gödel's stationary universe -- 3. Gödel's expanding universes -- 4. Resulting studies of causality -- 5. Resulting studies of universe models -- 6. The singularity theorems -- 7. Gödel's dialogue with Einstein -- References -- Kurt Gödel and the constructive Mathematics of A.A. Markov -- References -- Hao Wang as Philosopher -- 1. Style, convictions, and method -- 2. The concept of set -- 3. Minds and machines -- 4. Wang on "analytic empiricism"--5. Conclusion -- References -- A bottom-up approach to foundations of mathematics * -- 1. Introduction -- 2. Basic concepts -- 3. Independent sentences -- 4. Bounded arithmetic -- 5. Relations to computational complexity -- 6. Prepositional calculus -- 7. Model theory of weak arithmetical theories -- 8. Conclusions -- References -- K-graph Machines: generalizing Turing's machines and arguments* -- Introduction -- 1. Turing's Analysis -- 2. Post Productions & Puzzles -- 3. K-Graph Machines -- 4. Subsumption and Simulation -- 5. Concluding Remarks -- References
Cover -- Half-title -- Series information -- Title page -- Copyright information -- Table of contents -- Preface -- Part I Invited Papers -- Gödel's program for new axioms: Why, where, how and what? -- 1. Why new axioms? -- 2. Where should one look for new axioms? -- 3. How is the unfolding of a system defined? -- 4. The expansive closure of non-flnitist arithmetic: what's obtained -- 5. The unfolding of set theory -- References -- Infinite-valued Gödel Logics with 0-1-Projections and Relativizations* -- 1. Introduction -- 2. Propositional Gödel logics -- 3. Completeness of propositional Gödel logics with projections -- 4. First-order Gödel logics -- 5. Incompleteness of first-order Gödel logics with 0-1-projections and relativizations -- 6. Conclusion -- References -- Contributions of K. Gödel to Relativity and Cosmology* -- 1. Introduction -- 2. Gödel's stationary universe -- 3. Gödel's expanding universes -- 4. Resulting studies of causality -- 5. Resulting studies of universe models -- 6. The singularity theorems -- 7. Gödel's dialogue with Einstein -- References -- Kurt Gödel and the constructive Mathematics of A.A. Markov -- References -- Hao Wang as Philosopher -- 1. Style, convictions, and method -- 2. The concept of set -- 3. Minds and machines -- 4. Wang on "analytic empiricism"--5. Conclusion -- References -- A bottom-up approach to foundations of mathematics * -- 1. Introduction -- 2. Basic concepts -- 3. Independent sentences -- 4. Bounded arithmetic -- 5. Relations to computational complexity -- 6. Prepositional calculus -- 7. Model theory of weak arithmetical theories -- 8. Conclusions -- References -- K-graph Machines: generalizing Turing's machines and arguments* -- Introduction -- 1. Turing's Analysis -- 2. Post Productions & Puzzles -- 3. K-Graph Machines -- 4. Subsumption and Simulation -- 5. Concluding Remarks -- References