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The Discovery Of My Completeness Proofs
 Bulletin of Symbolic Logic
, 1996
"... This paper deals with aspects of my doctoral dissertation 1 ..."
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This paper deals with aspects of my doctoral dissertation 1
For Per Lindström My route to arithmetization
"... I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of ..."
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I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of
Some Topics in System Theory
, 1970
"... The foundations of measurement theory were invesUgated by modeltheoreUc methods. The purpose was to establish a firm ba~is for <;leneral system theory. One major result was the formulatton of the concepts of scale, scale transformation and the proof of the existence, for an arbitrary scale, of th ..."
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The foundations of measurement theory were invesUgated by modeltheoreUc methods. The purpose was to establish a firm ba~is for <;leneral system theory. One major result was the formulatton of the concepts of scale, scale transformation and the proof of the existence, for an arbitrary scale, of the group of scale transformatiqns which "leave the scale form invariantII. As an illustration of the appUcabiUty of these concepts and because of its intrinsic interest an expo~ition was <;liven of the theory of measurement for extensive quantities. A novel formulation of the usual axioms was developed which made them ~lementary formulae in the first order predicate calculus. Thus it was P9ssible to show that this theory is modelcomplete 0 Then A. Robinson I f! tlleorems were applied to show that this theory is negation complete. In the formulation of the existence theorem for scale transformation 1 groups no restriction was placed on the empirical 'Emodel Qr the numerical 'Emodel and in the other illustrative examples it wa $ shown how different choices of these 'Emodels lead to different scale transformation groups. An example of a theory of a nonextensive quantity was presented but the methods used before would not Yield modelcompleteness for this theory and thus an interesting unsolved problem remains.
GÖDEL’S COMPLETENESS THEOREM WITH NATURAL LANGUAGE FORMULAS
"... We give a selfcontained proof of the GÖDEL completeness theorem based on natural language. Utilizing a naive understanding of language, the semantics of natural language formulas is intuitively clear, which makes the correctness of our natural deduction style proof calculus immediate. The conver ..."
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We give a selfcontained proof of the GÖDEL completeness theorem based on natural language. Utilizing a naive understanding of language, the semantics of natural language formulas is intuitively clear, which makes the correctness of our natural deduction style proof calculus immediate. The converse direction, including a HENKINstyle model construction, is more involved, but hopefully natural as well. 1