Proof, Computation, Complexity 2016
Abstracts of the invited speakers of PCC
- Dag Normann, Univ. of Oslo, Norway: Revisiting Transfinite Types
- In this talk I will reconstruct spaces of countable and uncountable transfinite types, this time using limit spaces. This approach turns out to give a better access to internal concepts of computability for such spaces.
The talk will be a report on ongoing research. This research is rooted in earlier work by Ulrich Berger and by myself, and the revisiting is inspired by recent contributions by Selivanov, Schröder and de Brecht.
- Paulo Oliva, Queen Mary Univ. London, UK: Modified bar recursion - 15 years on
- I remember as if it was yesterday when during the second year (2001) of my PhD studies we had a visitor
giving a talk about “modified bar recursion”. I had just learnt about Spector bar recursion from
Kohlenbach and was quite intrigued by what kind of different form of bar recursion one could come
up with. The speaker was Ulrich Berger, and that talk would shape much of what I have been doing
since then. I went on to visit Ulrich in Swansea, and had the honour to co-author two papers [1,2] with
him on this new form of bar recursion. In this talk I hope to look back at that work, and much of
what followed, in terms of inter-definability results  and novel connections to Game Theory via the
recent work on selection functions [4,5].
 Ulrich Berger and Paulo Oliva, Modified bar recursion, MSCS, 16(2):163-183, 2006
 Ulrich Berger and Paulo Oliva, Modified bar recursion and classical dependent choice, LNL, 20:89-107, 2005
 Thomas Powell, The equivalence of bar recursion and open recursion, APAL, 165(11):1727-1754, 2014
 Martín Escardó and Paulo Oliva, Bar recursion and products of selection functions, JSL, 80(1):1-28, 2015
 Martín Escardó and Paulo Oliva, Sequential games and optimal strategies, Proc. of the Royal Society A, 467:1519-1545, 2011
- Thomas Streicher, Technical University Darmstadt, Germany: An effective Spectral Theorem for bounded self adjoint operators
- Using (sort of) abstract methods from topological domain theory we prove
that the spectral theorem for bounded selfadjoint operators is effective in the sense of TTE, i.e., it holds in the Kleene Vesley topos.
We also identify the natural topology on the involved spaces induced by their effective representations.
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Last modified (date in French): dim. mai 1 21:39:10 CEST 2016