The Bristol model:An abyss called a Cohen real

We construct a model M of ZF which lies between L and L[c] for a Cohen real c and does not have the form L(x) for any set x. This is loosely based on the unwritten work done in a Bristol workshop about Woodin's HOD Conjecture in 2011. The construction given here allows for a finer analysis of the needed assumptions on the ground models, thus taking us one step closer to understanding models of ZF, and the HOD Conjecture and its relatives. This model also provides a positive answer to a question of Grigorieff about intermediate models of ZF, and we use it to show the failure of Kinna-Wagner Principles in ZF

Generalized Effective Reducibility

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considerung the effective equivalence of various versions of the axiom of choice

Abnormal activity in the precuneus during time perception in Parkinson’s disease: An fMRI study

Background Parkinson's disease (PD) patients are deficient in time estimation. This deficit improves after dopamine (DA) treatment and it has been associated with decreased internal timekeeper speed, disruption of executive function and memory retrieval dysfunction. Methodology/Findings The aim of the present study was to explore the neurophysiologic correlates of this deficit. We performed functional magnetic resonance imaging on twelve PD patients while they were performing a time reproduction task (TRT). The TRT consisted of an encoding phase (during which visual stimuli of durations from 5s to 16.6s, varied at 8 levels were presented) and a reproduction phase (during which interval durations were reproduced by a button pressing). Patients were scanned twice, once while on their DA medication (ON condition) and once after medication withdrawal (OFF condition). Differences in Blood-Oxygenation-Level-Dependent (BOLD) signal in ON and OFF conditions were evaluated. The time course of activation in the brain areas with different BOLD signal was plotted. There were no significant differences in the behavioral results, but a trend toward overestimation of intervals ≤11.9s and underestimation of intervals ≥14.1s in the OFF condition (p<0.088). During the reproduction phase, higher activation in the precuneus was found in the ON condition (p<0.05 corrected). Time course was plotted separately for long (≥14.1s) and short (≤11.9s) intervals. Results showed that there was a significant difference only in long intervals, when activity gradually decreased in the OFF, but remained stable in the ON condition. This difference in precuneus activation was not found during random button presses in a control task. Conclusions/Significance Our results show that differences in precuneus activation during retrieval of a remembered duration may underlie some aspects of time perception deficit in PD patients. We suggest that DA medication may allow compensatory activation in the precuneus, which results in a more accurate retrieval of remembered interval duration

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

Moving up and down in the generic multiverse

We give a brief account of the modal logic of the generic multiverse, which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a ground model of". The fragment of the first relation is called the modal logic of forcing and was studied by us in earlier work. The fragment of the second relation is called the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments.Comment: 10 pages. Extended abstract. Questions and commentary concerning this article can be made at http://jdh.hamkins.org/up-and-down-in-the-generic-multiverse

Beginning of stability theory for Polish Spaces

We consider stability theory for Polish spaces and more generally for definable structures. We succeed to prove existence of indiscernibles under reasonable conditions

The NESTOR Framework: how to Handle Hierarchical Data Structures

Περιέχει το πλήρες κείμενοIn this paper we study the problem of representing, managing and exchanging hierarchically structured data in the context of a Digital Library (DL). We present the NEsted SeTs for Object hieRarchies (NESTOR) framework defining two set data models that we call: the “Nested Set Model (NS-M)” and the “Inverse Nested Set Model (INSM)” based on the organization of nested sets which enable the representation of hierarchical data structures. We present the mapping between the tree data structure to NS-M and to INS-M. Furthermore, we shall show how these set data models can be used in conjunction with Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH) adding new functionalities to the protocol without any change to its basic functioning. At the end we shall present how the couple OAI-PMH and the set data models can be used to represent and exchange archival metadata in a distributed environment

Improving brain imaging in Parkinson's disease by accounting for simultaneous motor output

Parkinson's disease leads to a variety of movement impairments. While studying the disease with fMRI, the main motivation for the research becomes one of its major obstacles: the motor output is unpredictable. Therefore it is troublesome to access, inside the scanner, performances of motor tasks and reliably relate them to brain measurements. We proposed to overcome this by expanding the patients’ number and restricting statistical criteria from a previous study which used a glove with non-magnetic sensors during scanning. Our results revealed basal ganglia not observed in the previous study confirming the usefulness of the device in fMRI studies