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Previous Paris-Harrington post
[Ed. note: This post was essentially ready two years ago, but I got distracted with other matters. If you’re seeing this for the first time, or want to refresh your memory, posts 8 and 9 introduced the Paris-Harrington theorem. Posts 21 through 24 continued the discussion, in a dialog with Bruce Smith. MW]
Filed under Conversations, Peano Arithmetic
MW: Last time we learned about the “back-and-forth” condition for two countable structures M and N for a (countable) language L:
Filed under Conversations, Peano Arithmetic
MW: Time to finish off Enayat’s Theorem 7:
Theorem 7: Every countable recursively saturated model N of PA+ΦT is a T-standard model of PA.
Filed under Conversations, Peano Arithmetic
MW: We’re still going through Enayat’s proof of his Theorem 7:
Theorem 7: Every countable recursively saturated model N of PA+ΦT is a T-standard model of PA.
Filed under Conversations, Peano Arithmetic
MW: I ended the last post with a puzzle. Here it is again, in more detail.
Filed under Conversations, Peano Arithmetic
MW: Enayat’s second major result is:
Theorem 7: Every countable recursively saturated model of PA+ΦT is a T-standard model of PA.
Filed under Conversations, Peano Arithmetic
MW: Continuing the recap… Continue reading
Filed under Peano Arithmetic
MW: It’s been ages since John Baez and I discussed Enayat’s paper—not since October 2020! John has since moved on to fresh woods and pastures new. I’ve been reading novels. But I feel I owe it to our millions of readers to finish the tale, so here goes.
Filed under Peano Arithmetic
Every specialty has its tricks of the trade. They become second nature to practitioners, so they often don’t make it into the textbooks. Quantifiers rule in logic; here are some of the games we can play with them. I’ll start with tricks that apply in logic generally, then turn to those specific to Peano arithmetic.
Filed under Peano Arithmetic
Diagonal Argument 