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This is a question from Stephan Belniuk's Stefan Bilaniuk's very good free online book "A Problem Course in Mathematical Logic"Logic: Problem 18.6. Suppose Sigma$\Sigma$ is a recursive set of sentences of LN. Find a sentence of LN, which we'll denote by Con(Sigma), $Con(\Sigma)$, such that Sigma$\Sigma$ is consistent if and only if $A |- Con(Sigma)\vdash Con(\Sigma)$. By Godel's second incompleteness theorem isn't this impossible? |
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Statement of consistency in Godel's second incompleteness theoremThis is a question from Stephan Belniuk's very good free online book "A Problem Course in Mathematical Logic": Problem 18.6. Suppose Sigma is a recursive set of sentences of LN. Find a sentence of LN, which we'll denote by Con(Sigma), such that Sigma is consistent if and only if A |- Con(Sigma). By Godel's second incompleteness theorem isn't this impossible?
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