I would like to inform that at "Logic Colloquium 2009" (31 July - 5 August, 2009, Sofia, Bulgaria) I, together with dr Teodor J. Stepien, delivered a talk. During this talk we presented a sketch of the proof of the consistency of Peano's Arithmetic System (of course, the FULL proof was constructed by us before the mentioned Conference "Logic Colloquium 2009"). This proof is completely ELEMENTARY, i.e. there are used ONLY the axioms of first-order logic and the axioms of Peano's Arithmetic System. Hence, from the construction of this proof, it follows that Gödel's Second Incompleteness Theorem is INVALID. The abstract of this talk was published in "The Bulletin of Symbolic Logic": T. J. Stepien and L. T. Stepien, Bull. Symb. Logic16, No. 1, 132 (2010). URL:

## The consistency of Peano Arithmetic System

I would like to inform that at "Logic Colloquium 2009" (31 July - 5 August, 2009, Sofia, Bulgaria) I, together with dr Teodor J. Stepien, delivered a talk. During this talk we presented a sketch of the proof of the consistency of Peano's Arithmetic System (of course, the FULL proof was constructed by us before the mentioned Conference "Logic Colloquium 2009"). This proof is completely ELEMENTARY, i.e. there are used ONLY the axioms of first-order logic and the axioms of Peano's Arithmetic System. Hence, from the construction of this proof, it follows that Gödel's Second Incompleteness Theorem is INVALID. The abstract of this talk was published in

"The Bulletin of Symbolic Logic": T. J. Stepien and L. T. Stepien,Bull. Symb. Logic16, No. 1, 132 (2010). URL:www.math.ucla.edu/~asl/bsl/1601/1601-004.ps

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