Titlebook: Logic, Foundations of Mathematics, and Computability Theory; Part One of the Proc Robert E. Butts,Jaakko Hintikka Conference proceedings 19

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Logic, Foundations of Mathematics, and Computability Theory978-94-010-1138-9Series ISSN 1566-659X Series E-ISSN 2215-1974

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Ineffability Properties of Cardinals IIarge cardinal’ properties are better viewed as properties of normal ideals than as properties of cardinals alone, and that in order to understand these properties fully it is necessary to consider the associated normal ideals.

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Some Purely Mathematical Results Inspired by Mathematical Logic continuum hypothesis and numerous results about algorithmical unsolvability of many important decision problems in mathematics. However, these results are not purely mathematical since their very formulations involve some logical notions such as the notion of axiomatic theory or that of algorithm.

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Constructions ‘by Finite’My talk’s aim is a description and some grounds for one natural ‘good’ model C of finite type functional over the natural numbers N. In this respect the talk is like D. Scott’s report [10] on natural model for type-free λ-calculus at the last Congress.

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Some Eastern Two Cardinal TheoremsA more descriptive title of this paper might be ‘Elaborations on Morley’s proof of Vaught’s gap ω two cardinal theorem’. The title given above comes from the main result of Section 2, possibly the most interesting result of the paper. Let us begin by introducing some terminology and stating Vaught’s Theorem.

Intervention

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Algorithmic Logic, a Tool for Investigations of ProgramsThe paper shows a method of connecting formulas (of new type) with the properties of a program. Metamathematical studies of the algorithmic logic obtained in this way lead to a uniform approach to all the methodological problems connected with programming.

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The Western Ontario Series in Philosophy of Sciencehttp://image.papertrans.cn/l/image/588040.jpg

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1566-659X the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of 978-94-010-1138-9Series ISSN 1566-659X Series E-ISSN 2215-1974

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