Con(PA) means the consistency of PA. It can be formalized within PA as a statement about integers, something like “there’s no integer encoding a proof in PA that 1=0”.
For an explanation of Nesov’s counterintuitive statement that PA+NOT(Con(PA)) is a consistent theory (or rather, equiconsistent with PA itself), see paragraph 48.2 in this PDF. For an explanation of how to build a model for that preposterous theory, see paragraph 2.1 in this PDF.
Con(PA) means the consistency of PA. It can be formalized within PA as a statement about integers, something like “there’s no integer encoding a proof in PA that 1=0”.
For an explanation of Nesov’s counterintuitive statement that PA+NOT(Con(PA)) is a consistent theory (or rather, equiconsistent with PA itself), see paragraph 48.2 in this PDF. For an explanation of how to build a model for that preposterous theory, see paragraph 2.1 in this PDF.