Difference between revisions of "Peano's Parlour"

From Peano's Parlour
Jump to: navigation, search
Line 1: Line 1:
 
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.  
 
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.  
  
1. [[Cuts in models of PA and independence results]]
+
[[Cuts in models of PA and independence results]]
  
2. [[Recursively saturated, resplendent models, and saturated models.]]
+
[[Recursively saturated, resplendent models, and saturated models.]]
 
+
3. [[Automorphisms and automorphism groups.]]
+
 
   
 
   
4. [[Standard systems and the Scott set problem.]]
+
[[Standard systems and the Scott set problem.]]
 
   
 
   
5. [[Lattices of elementary substructures.]]
+
[[Lattices of elementary substructures.]]
 
   
 
   
6. [[Uncountable models with interesting second-order properties.]]
+
[[Uncountable models with interesting second-order properties.]]
 
   
 
   
7. [[Nonstandard satisfaction classes.]]
+
[[Nonstandard satisfaction classes.]]
  
8. [[Model theory of strong fragments of arithmetic.]]
+
[[Model theory of strong fragments of arithmetic.]]
  
9. [[Model theory of weak fragments of arithmetic.]]
+
[[Model theory of weak fragments of arithmetic.]]
  
10. [[Model theoretic methods in proof theory.]]
+
[[Model theoretic methods in proof theory.]]
  
The last chapter of   Kossak, Roman; Schmerl, James H. The structure of models of Peano arithmetic. Oxford Logic Guides, 50. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2006. has a list of 20 questions with comments and references. Here is an [[errata]] for the book.
+
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.

Revision as of 09:01, 18 January 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.

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.