# Category Archives: Peano Arithmetic

## Nonstandard Models of Arithmetic 31

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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

## 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.

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## Topics in Nonstandard Arithmetic 10: Truth (Part 4)

Filed under Peano Arithmetic

## Nonstandard Models of Arithmetic 26

MW: Continuing the recap… Continue reading

Filed under Peano Arithmetic

## Nonstandard Models of Arithmetic 25

Previous Enayat post

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.