Lecture Notes in Logic, 49

Large Cardinals, Determinacy and Other Topics

The Cabal Seminar, Volume IV

Alexander S. Kechris, Benedikt Löwe, John R. Steel

The proceedings of the Los Angeles Caltech-UCLA ‘Cabal Seminar’ were originally published in the 1970s and 1980s. Large Cardinals, Determinacy and Other Topics is the final volume in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. This final volume contains Parts VII and VIII of the series. Part VII focuses on ‘Extensions of AD, models with choice’, while Part VIII (‘Other topics’) collects material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of the book collection of every set theorist.

Table of Contents

Preface

Original Numbering

Part VII. Extensions of AD, models with choice

1. A brief history of determinacy

2. “AD plus uniformization” is equivalent to “Half ADR”

3. The independence of DC from AD

4. Games of countable length

5. Some consistency results in ZFC using AD

6. Subsets of ℵ1 constructible from a real

7. AD and the uniqueness of the supercompact measures on ℘ꞷ1 (λ)

8. The extender algebra and Σ21-absoluteness

Part VIII. Other topics:

9. On Vaught’s conjecture

10. Capacities and analytic sets

11. More saturated ideals

12. The fourteen Victoria Delfino problems and their status in the year 2020

Bibliography