What is meant by v? : : reflections on the universe of all sets / / Tatiana Arrigoni.

• VerfasserIn: Arrigoni, Tatiana,
• Place / Publishing House: Paderborn, Germany : : Mentis,, [2007]; ©2007
• Year of Publication: 2007
• Language: English
• Physical Description: 1 online resource

That the structure V = UaVa be the universe of all sets, that the set theoretical axioms be true assertions about V or that a question like the Continuum Hypothesis be still open (since it is undecided whether it holds or fails in V) are common assertions in set theory. How one is to understand them, tough, is not an obvious matter. The aim of this book is just to interpret the façon de parler that V is the universe of all sets in a way that is faithful to what is actually done in set theory.

Table of Contents

Intro -- What is meant by V?: Reflections on the universe of all sets -- Contents -- PRELIMINARIES -- 1. INTRODUCING V -- 1.0. Preface -- 1.1 What's the problem with V? A sketch of the status quaestionis -- 1.2. The-real-universe-problem -- 1.3. The-choice-for-the-"right"-universe-problem -- 1.4. A heuristic approach to V. A note on Jensen's "pragmatic" point of view -- 1.5. V as framework for definitive achievements: examples -- 1.6. V as structure: an "interesting per se" and "large" place -- 1.7. V as epistemic attitude: the broadest possible point of view on sets -- 1.8. Prospect -- 2. V AND THE MAXIMUM ITERATIVE CONCEPT -- 2.0. PREFACE -- 2.1. The cumulative hierarchy V -- 2.2. The maximum iterative conception -- 2.3. What does it mean appealing to the maximum iterative concept? -- 2.4. What is at odds with the maximum iterative concept? -- 2.5. Is the maximum iterative concept dispensable? -- 2.6. What is the maximum iterative concept good for? -- 2.7. The mathematical practice of set theory -- Untitled -- 3. V AND LARGE CARDINAL AXIOMS -- 3.0. PREFACE -- 3.1. Intrinsic evidence for large cardinal hypothesis -- 3.2. Bottom up (extrinsic) evidence for large cardinal hypotheses -- 3.3 Epistemic features of intrinsic evidence -- 3.4. Concluding remarks on intrinsic and extrinsic evidence. -- 3.5. Large cardinal axioms and the concept of V as "the broadest possible point of view" -- 4. V, FORCING AND CH -- 4.0. Preface -- 4.1. Extending the universe of all sets -- 4.2. Transcending the universe of all sets? -- 4.3. Clarifying (possible) misunderstandings -- 4.4 Transcending forcing? -- EPILOGUE -- BIBLIOGRAPHY -- INDEX OF NAMES.