Two extremely active areas of modern mathematical logic are Computability Theory and Set Theory. These fields are intensively researched in many parts of the USA, Europe and Asia, including Singapore. One purpose of this programme is to bring leading researchers in these fields to the IMS for collaboration with researchers from Singapore and other parts of Asia. A second purpose is to develop newly-emerging and valuable connections between these fields. The result will be to strengthen cooperation between Singapore and research groups elsewhere, as well as to forge new connections between computability-theorists and set-theorists.
Some topics of great current interest in set theory are: cardinal characteristics, iterated forcing, large cardinals, cardinal arithmetic, the structure of HOD, descriptive set theory, inner model theory and determinacy.
Some topics of great current interest in computability are: local and global degree theory, algorithmic randomness, reverse mathematics and reverse recursion theory, higher recursion theory and higher randomness, recursive model theory.
Recently, important connections between these fields have emerged: computable descriptive set theory, computability theory for uncountable structures, forcing in computational complexity theory, complexity theory for computations on sets, infinite-time Turing machines.
Outline of Program Structure
Week 1 – 2 (30 March – 10 April 2015): Set theory (forcing, large cardinals, descriptive set theory)
Week 3 (13 – 17 April 2015): Interactions between set theory and computability theory (computational complexity in set theory, computational descriptive set theory, forcing in computational complexity theory, etc)
Week 4 – 5 (20 – 30 April 2015): Computability theory (degree theory, reverse mathematics, higher recursion theory)
- Raghavan Dilip (National University of Singapore)
- Sy David Friedman (University of Vienna)
- Yue Yang (National University of Singapore)