MW: Last time we learned about the “back-and-forth” condition for two countable structures M and N for a (countable) language L:
Category Archives: Peano Arithmetic
Nonstandard Models of Arithmetic 30
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.
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Nonstandard Models of Arithmetic 29
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
Nonstandard Models of Arithmetic 28
MW: I ended the last post with a puzzle. Here it is again, in more detail.
Filed under Conversations, Peano Arithmetic
Nonstandard Models of Arithmetic 27
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
Nonstandard Models of Arithmetic 26
MW: Continuing the recap… Continue reading
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Nonstandard Models of Arithmetic 25
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.
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Topics in Nonstandard Arithmetic 9: Tricks with Quantifiers
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.
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Topics in Nonstandard Arithmetic 8: Extensions and Substructures
Substructures and extensions loom large in math: subgroups, subrings, extension fields, submanifolds, subspaces of topological spaces… So too in the model theory of PA.
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Diagonal Argument 