Sets and Computations

The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures.

Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.

Contents:

• Set Theory:
  • Q (Jörg Brendle)
  • A Fraïssé Approach to the Poulsen Simplex (Clinton Conley and Asger Törnquist)
  • On the Set-Generic Multiverse (Sy-David Friedman, Sakaé Fuchino and Hiroshi Sakai)
  • Real Games and Strategically Selective Coideals (Paul B Larson and Dilip Raghavan)
• Interactions:
  • Cobham Recursive Set Functions and Weak Set Theories (Arnold Beckmann, Sam Buss, Sy-David Friedman, Moritz Müller and Neil Thapen)
  • Higher Randomness and lim-sup Forcing Within and Beyond Hyperarithmetic (Takayuki Kihara)
  • Ackermannian Goodstein Principles for First Order Peano Arithmetic (Andreas Weiermann)
  • Tracking Chains Revisited (Gunnar Wilken)
• Computation Theory:
  • Groups with Orderings of Arbitrary Algorithmic Complexity (Jennifer Chubb, Mieczyslaw K Dabkowski and Valentina Harizanov)
  • Measure Theory and Hilbert's Tenth Problem Inside Q (Russell Miller)

Readership: Researchers and graduate students in mathematical logic, especially those interested in set theory and recursion theory.
Set Theory;Computation Theory;Randomness;Computational Complexity;Proof Theory;Multiverse;Hilbert's Tenth ProblemKey Features:

• Suitable for graduate students as well as researchers who desire to learn more about mathematical logic