Baire spaces and infinite games

It is well known that if the nonempty player of the Banach-Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box topology. The converse of this implication may be true also: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.Comment: 21 page

Selection principles and countable dimension

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.Comment: 10 page

Speed and accuracy of dyslexic versus typical word recognition: an eye-movement investigation

Developmental dyslexia is often characterized by a dual deficit in both word recognition accuracy and general processing speed. While previous research into dyslexic word recognition may have suffered from speed-accuracy trade-off, the present study employed a novel eye tracking task that is less prone to such confounds. Participants (10 dyslexics and 12 controls) were asked to look at real word stimuli, and to ignore simultaneously presented non-word stimuli, while their eye-movements were recorded. Improvements in word recognition accuracy over time were modeled in terms of a continuous non-linear function. The words’ rhyme consistency and the non-words’ lexicality (unpronounceable, pronounceable, pseudohomophone) were manipulated within-subjects. Speed related measures derived from the model fits confirmed generally slower processing in dyslexics, and showed a rhyme consistency effect in both dyslexics and controls. In terms of overall error rate, dyslexics (but not controls) performed less accurately on rhyme-inconsistent words, suggesting a representational deficit for such words in dyslexics. Interestingly, neither group showed a pseudohomophone effect in speed or accuracy, which might call the task-independent pervasiveness of this effect into question. The present results illustrate the importance of distinguishing between speed- vs. accuracy related effects for our understanding of dyslexic word recognition

Remarks on countable tightness

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelof property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are further explored.Comment: Extended from 12 pages to 23 pages. Newly extended to 27 page