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Towards Abstractions for Distributed Systems
, 2004
"... For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equa ..."
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For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equally convincing formal foundation for distributed computing has not been forthcoming. This thesis seeks to contribute towards ameliorating that omission. To this end, guided by the assumption that distributed computing is concurrent computing with partial failures of various kinds, we extend the asynchronous calculus with a notion of sites, the possibility of site failure, a persistence mechanism to deal with site failures, the distinction between intersite and intrasite communication, the possibility of message loss in intersite communication and a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.
UNIFORM FAMILIES OF POLYNOMIAL EQUATIONS OVER A FINITE FIELD AND STRUCTURES ADMITTING AN EULER CHARACTERISTIC OF DEFINABLE SETS
, 2000
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"... This is a book about doing model theory without an underlying logical system. It teaches us how to live without concrete models, sentences, satisfaction and so on. Our approach is based upon the theory of institutions, which has witnessed a vigorous and systematic development over the past two decad ..."
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This is a book about doing model theory without an underlying logical system. It teaches us how to live without concrete models, sentences, satisfaction and so on. Our approach is based upon the theory of institutions, which has witnessed a vigorous and systematic development over the past two decades and which provides an ideal framework for true abstract model theory. The concept of institution formalizes the intuitive notion of logical system into a mathematical object. Thus our model theory without underlying logical systems and based upon institution theory may be called ‘institutionindependent model theory’. Institutionindependent model theory has several advantages. One is its generality, since it can be easily applied to a multitude of logical systems, conventional or less conventional, many of the latter kind getting a proper model theory for the first time through this approach. This is important especially in the context of the recent high proliferation of logics in computing science, especially in the area of formal specification. Then there is the advantage of illuminating the model theoretic phenomena and its subtle network of causality relationships, thus leading to a deeper understanding which produces new
1.1. Definitions 2
, 2002
"... 1. Classification of Banach spaces by dimension 2 ..."
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