Skip to main content
MathOverflow

Return to Question

edited title
Link
Joel David Hamkins
Joel David Hamkins
  • 236.3k
  • 44
  • 777
  • 1.4k

Are there mutually independent undecidable statements?

Became Hot Network Question
Adding round brackets
Source Link
edit approved Feb 26 at 21:04
Marco Ripà
edit approved Feb 26 at 21:04
Marco Ripà
  • 1.5k
  • 5
  • 19

In a recursively axiomatized theory such as PA, are there undecidable statements that are arithmetically true but which are mutually independent ? I(i.e., are there two statements A and B that are each undecidable from the axioms and where neither is deducible from the other  ?)?

In a recursively axiomatized theory such as PA, are there undecidable statements that are arithmetically true but which are mutually independent ? I.e. are there two statements A and B that are each undecidable from the axioms and where neither is deducible from the other  ?

In a recursively axiomatized theory such as PA, are there undecidable statements that are arithmetically true but mutually independent (i.e., are there two statements A and B that are each undecidable from the axioms and where neither is deducible from the other?)?

Source Link
Jacques Sentier
Jacques Sentier
  • 111
  • 4

Are there mutually independent undecidable statements

In a recursively axiomatized theory such as PA, are there undecidable statements that are arithmetically true but which are mutually independent ? I.e. are there two statements A and B that are each undecidable from the axioms and where neither is deducible from the other ?