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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Non-Standard Analysise sense, ‘the same properties’ as the natural numbers. The title of Skolem’s paper indicates that the purpose of it was to show that no axiomatic system specified in a formal language, in Skolem’s case the lower predicate calculus, can characterize the natural numbers categorically. At that time, ho

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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.

Ligament

Interpretability of Elementary Theories of groups formalised without a neutral element symbol is a proper subtheory of that formalised in a language with a symbol for this element. We may observe an even more striking situation in geometry: the systems presented in Pieri (1908) and Tarski (1959) using different primitive notions are comp

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Categorical Foundations and Foundations of Category Theoryations of mathematics, in preference to current foundational schemes. An opposite view is argued here on the grounds that the notions of operation and collection are prior to all structural notions. However, no position is taken as to whether such are to be conceived extensionally or intensionally..

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Basic Concepts of Computer Science and Logiccomputer field, are presented. The sole aim of this paper is to attempt to bridge the gulf between the computer field on the one hand, and mathematics and logic on the other. The particular concepts are presented here for justification only: and therefore almost no theorems are included. (Fortunatel