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Automorphisms of Short Saturated Models of PA

Automorphisms of Short Saturated Models of PA. Ermek Nurkhaidarov (Penn State) & Erez Shochat (St. Francis College)*. Saturated and Boundedly Saturated Models of PA. Saturated and Boundedly Saturated Models of PA. Saturated and Boundedly Saturated Models of PA.

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Automorphisms of Short Saturated Models of PA

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  1. Automorphisms of Short Saturated Models of PA Ermek Nurkhaidarov (Penn State) & Erez Shochat (St. Francis College)*

  2. Saturated and Boundedly Saturated Models of PA

  3. Saturated and Boundedly Saturated Models of PA

  4. Saturated and Boundedly Saturated Models of PA

  5. Saturated and Boundedly Saturated Models of PA

  6. Saturated and Boundedly Saturated Models of PA

  7. Facts:

  8. Facts:

  9. Facts:

  10. Facts:

  11. Short Models

  12. Short Models

  13. Short Models

  14. Short Models

  15. Short Saturated Models of PA

  16. Short Saturated Models of PA

  17. Short Saturated Models of PA

  18. Short Saturated Models of PA

  19. Short Saturated Models of PA

  20. Automorphisms of Short Saturated Models of PA

  21. Automorphisms of Short Saturated Models of PA

  22. Automorphisms of Short Saturated Models of PA

  23. Sketch of Proof • Lemma: Every automorphism of a short saturated model which sends coded sets to coded sets can be extended to an automorphism of the saturated model. (“back-and-forth”)

  24. Sketch of Proof • Lemma: Every automorphism of a short saturated model which sends coded sets to coded sets can be extended to an automorphism of the saturated model. (“back-and-forth”) • Remains to show: Lemma: Every automorphism of a short saturated model sends coded sets to coded sets.

  25. Sketch of Proof of Lemma

  26. Sketch of Proof of Lemma

  27. Sketch of Proof of Lemma

  28. Sketch of Proof of Lemma

  29. Sketch of Proof of Lemma

  30. Main Results

  31. Main Results

  32. Main Results

  33. Main Results

  34. All these results and more are to appear in a future issue of the Notre Dame Journal of Formal Logic, in the paper:

  35. Thank You!

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