Essays about: "Gödel s Theorem"
Found 1 essay containing the words Gödel s Theorem.
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1. A Model-Theoretic Proof of Gödel's Theorem : Kripke's Notion of Fulfilment
University essay from Stockholms universitet/Matematiska institutionenAbstract : The notion of fulfilment of a formula by a sequence of numbers, an approximation of truth due to Kripke, is presented and subsequently formalised in the weak arithmetic theory IΣ1, in some detail. After a number of technical results connecting the formalised notion to the meta-theoretical one a version of Gödel’s Incompleteness Theorem, that no consistent, recursively axiomatisable, Σ2-sound extension T of Peano arithmetic is complete, is shown by construction of a true Π2-sentence and a model of T where it is false, yielding its independence from T. READ MORE