Difference between revisions of "Peano's Parlour"

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This will be an awesome models of Peano Arithmetic Wiki :)...
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This site is dedicated to open problems in nonstandard models of Peano Arithmetic and related theories. As in most areas of mathematics, we do not suffer from a shortage of open problems. The problems are arranged by topics.  
Let's try to do math: $2^\kappa=\kappa$
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== Submit a problem, solve a problem ==
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[[Cuts in models of PA and independence results]].
This site is dedicated to open problems in nonstandard models of Paeno Arithmetic and related theory. As in most areas, we do not suffer from a shortage of open problems. The problems are arranged by category. Here is the list of categories.
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1. Cuts in models of PA and independence results
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[[Recursively saturated, resplendent models, and saturated models]].
 
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2. Recursively saturated, resplendent models, and saturated models.
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3. Automorphisms and automorphism groups.
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4. Standard systems and the Scott set problem.
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[[Standard systems and the Scott set problem]].
 
   
 
   
5. Lattices of elementary substructures.
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[[Lattices of elementary substructures]].
 
   
 
   
6. Uncounrtable models with interesting second-order properies.
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[[Uncountable models with interesting second-order properties]].
 
   
 
   
7. Nonstandard satisfaction classes.
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[[Nonstandard satisfaction classes]].
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[[Complexity and classification of countable models]].
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[[Automoprhism groups]].
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[[Model theory of strong fragments of arithmetic]].
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[[Model theory of weak fragments of arithmetic]].
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[[Model theoretic methods in proof theory]].
  
8. Model theory of strong fragments of arithmetic.
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The last chapter of ''The structure of models of Peano arithmetic'' by Kossak and Schmerl has a list of 20 questions with comments and references. Here is an [[errata]] for the book.
  
9. Model theory of weak fragments of arithmetic.
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== Contributing to Peano's Parlour ==
  
10. Model theoretic methods in proof theory.
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All registered members can contribute to problems/solutions/corrections/remarks. To register, send an email to the webmaster Victoria Gitman at vgitman@nylogic.org.  To contribute without registering, send an email to Victoria Gitman  or to Roman Kossak at rkossak@nylogic.org.

Latest revision as of 15:31, 6 February 2013

This site is dedicated to open problems in nonstandard models of Peano Arithmetic and related theories. As in most areas of mathematics, we do not suffer from a shortage of open problems. The problems are arranged by topics.

Cuts in models of PA and independence results.

Recursively saturated, resplendent models, and saturated models.

Standard systems and the Scott set problem.

Lattices of elementary substructures.

Uncountable models with interesting second-order properties.

Nonstandard satisfaction classes.

Complexity and classification of countable models.

Automoprhism groups.

Model theory of strong fragments of arithmetic.

Model theory of weak fragments of arithmetic.

Model theoretic methods in proof theory.

The last chapter of The structure of models of Peano arithmetic by Kossak and Schmerl has a list of 20 questions with comments and references. Here is an errata for the book.

Contributing to Peano's Parlour

All registered members can contribute to problems/solutions/corrections/remarks. To register, send an email to the webmaster Victoria Gitman at vgitman@nylogic.org. To contribute without registering, send an email to Victoria Gitman or to Roman Kossak at rkossak@nylogic.org.