Logic Colloquium '95

Combinatorial Principles from Adding Cohen Reals -- 1 Introduction -- 2 The combinatorial principles -- 3 Consistency of the principles in the Cohen model -- 4 Applications -- References -- Extensions of Models of PV -- Introduction -- 1 Preliminaries -- 2 An ultrapower -- 3 A compactness argument -- 4 A Boolean-valued extension -- 5 A construction of a counter-example function -- References -- Convergence Laws for Random Graphs -- 1 Background -- 2 Recursive Logics and Infinitary Logics -- 3 Random Graphs -- 4 Future Directions -- References -- V=L and Maximize -- 1 Naturalism -- 2 Maximize and Unify -- 3 Why V=L is restrictive -- 4 What goes wrong -- References -- Towards a Categorical Foundation of Mathematics -- 1. Introduction -- 2. The universe and the language -- 3. Abstract sets -- 4. Functions, categories and isomorphisms -- 5. A revision of category theory -- 6. 2-dimensional categories -- 7. Higher dimensional categories -- 8. Dependent types -- 9. Formal systems -- 10. Equivalence in FOLDS -- 11. In variance under L-equivalence -- References -- Strongly Minimal Sets and Geometry -- 1 Strongly minimal sets and pregeometries -- 2 Families of plane curves -- 3 Algebraic structure -- 4 Zariski geometries -- 5 The Mordell-Lang conjecture for function fields -- References -- Computationally-Sound Proofs -- 1 Introduction -- 2 Prior Notions and New Goals -- 2.1 Prior Notions of a Proof -- 2.2 Complexity, Polynomial Time and Classical Proofs -- 2.3 New Goals For Efficient Proofs -- 3 Computationally-Sound Proofs -- 3.1 CS Proofs With A Random Oracle -- 3.2 CS Proofs with a Random String -- 3.3 Deterministic CS Proofs -- 4 Certified Computation -- 5 Final Remarks -- 6 Acknowledgments -- References -- Lambek Calculus and Formal Languages -- Introduction -- 1 Preliminaries -- 2 Lambek grammars recognize context-free languages