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nLab > Latest Changes: Iterated inductive definitions

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    • CommentRowNumber1.
    • CommentAuthorUlrik
    • CommentTimeOct 21st 2016

    I’ve created iterated inductive definitions to record the definition (in response to this MO question). I also put a link to this page from ordinal analysis.

    • CommentRowNumber2.
    • CommentAuthorgnivasch
    • CommentTimeOct 23rd 2016
    Thanks!

    Could you give me a simple example of an inductive definition and how it helps in doing something useful with it? I think that might help me understand what is going on...

    Thanks,
    Gabriel Nivasch
    • CommentRowNumber3.
    • CommentAuthorUlrik
    • CommentTimeOct 26th 2016

    I’ve added the example of constructive tree ordinals.

    I’ve also changed the notation slightly to hopefully make everything a bit more intuitive. I also added a reference to Girard’s work on iterated inductive definitions.

    • CommentRowNumber4.
    • CommentAuthorgnivasch
    • CommentTimeOct 27th 2016
    What do the curly braces mean in {x-1} in equation (6)?

    Thanks again.
    • CommentRowNumber5.
    • CommentAuthorUlrik
    • CommentTimeOct 27th 2016

    The notation {e}(n)\{e\}(n) is just the usual short-hand for “the value of the partial recursive function with index ee on input nn” (and this value exists). This can elaborated into uses of Kleene’s T and U; feel free to add such an elaboration to the entry (or a reference).

1 to 5 of 5

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