Podcast
Questions and Answers
What is the significance of Gentzen's theory in relation to first-order Peano arithmetic (PA)?
What is the significance of Gentzen's theory in relation to first-order Peano arithmetic (PA)?
- Gentzen's theory is stronger than PA.
- Gentzen's theory is a subtheory of PA.
- Gentzen's theory is a weaker theory than PA.
- Gentzen's theory is incomparable to PA. (correct)
What can be proved in Gentzen's theory that cannot be proved in PA?
What can be proved in Gentzen's theory that cannot be proved in PA?
- The consistency of PA. (correct)
- Ordinary mathematical induction for all formulae.
- The completeness of PA.
- The inconsistency of PA.
What is the significance of the notion of interpretability?
What is the significance of the notion of interpretability?
- It is used to prove the inconsistency of a theory.
- It is used to show the completeness of a theory.
- It is used to compare the strength of two theories. (correct)
- It is used to prove the consistency of a theory.
What can be conclude about theory T if it is interpretable in another theory B?
What can be conclude about theory T if it is interpretable in another theory B?
What is the consequence of the second incompleteness theorem?
What is the consequence of the second incompleteness theorem?
What is the relationship between the consistency of theory T and theory B if T is interpretable in B?
What is the relationship between the consistency of theory T and theory B if T is interpretable in B?
What is the idea that motivates the use of interpretability to compare theories?
What is the idea that motivates the use of interpretability to compare theories?
What does Pudlák's result state about a consistent theory T that contains Robinson arithmetic, Q?
What does Pudlák's result state about a consistent theory T that contains Robinson arithmetic, Q?
What is true about Q+Con(T) and T, according to the arithmetized completeness theorem?
What is true about Q+Con(T) and T, according to the arithmetized completeness theorem?
Why can't PA interpret Gentzen's theory, according to Pudlák's result?
Why can't PA interpret Gentzen's theory, according to Pudlák's result?
What is true about Gentzen's theory and PA, in terms of consistency strength?
What is true about Gentzen's theory and PA, in terms of consistency strength?
What is required for a theory to be stronger than another theory, in terms of consistency strength?
What is required for a theory to be stronger than another theory, in terms of consistency strength?
