Easton supported Jensen coding and projective measure without projective Baire

We prove that it is consistent relative to a Mahlo cardinal that all sets of reals definable from countable sequences of ordinals are Lebesgue measurable, but at the same time, there is a $\Delta^1_3$ set without the Baire property. To this end, we introduce a notion of stratified forcing and stratified extension and prove an iteration theorem for these classes of forcings. Moreover we introduce a variant of Shelah's amalgamation technique that preserves stratification. The complexity of the set which provides a counterexample to the Baire property is optimal.Comment: 142 page

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

Continuous Family of Invariant Subspaces for R-diagonal Operators

We show that every R-diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu's S-transform is multiplicative. Our considerations base on a new concept of R-diagonality with amalgamation, for which we give several equivalent characterizations.Comment: 35 page

Amalgamation, absoluteness, and categoricity

"Vegeu el resum a l'inici del document del fitxer adjunt"

Roman roads: The hierarchical endosymbiosis of cognitive modules

Serial endosymbiosis theory provides a unifying paradigm for examining the interaction of cognitive modules at vastly different scales of biological, social, and cultural organization. A trivial but not unimportant model associates a dual information source with a broad class of cognitive processes, and punctuated phenomena akin to phase transitions in physical systems, and associated coevolutionary processes, emerge as consequences of the homology between information source uncertainty and free energy density. The dynamics, including patterns of punctuation similar to ecosystem resilience transitions, are large dominated by the availability of 'Roman roads' constituting channels for the transmission of information between modules

Computability Theory

Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from Gödel’s Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science