[FOM] speaking of provability logic
sambin
sambin at math.unipd.it
Tue May 22 03:29:04 EDT 2012
Dick de Jongh's original proof in 1975 also used Kripke semantics. It
was reported in a paper by Craig Smorynski some years later. While the
proof by Reidhaar-Olson follows some ideas from mine (see Boolos' book,
pages 111-113), de Jongh's proof followed a totally different approach,
as far as I recall. Perhaps one should ask de Jongh and/or Smorynski to
have more information.
Giovanni
On Mon, 21 May 2012 23:24:31 +0300, jkennedy at mappi.helsinki.fi wrote:
> Thanks Giovanni! Is this was the first proof that used Kripke
> semantics?
>
> Best,
>
> Juliette
>
>
> Quoting "Giovanni Sambin" <sambin at math.unipd.it>:
>
>> Dear Juliette,
>> the content of that paper appears also in Boolos' book "The logic of
>> provability". I recall that George Boolos was satisfied with this
>> piece of work by his student Lisa Reidhaar-Olson. In fact, she
>> provides a proof of the fixed point theorem which makes use of Kripke
>> semantics, which George considered clearer than my own original
>> syntactic proof.
>> This is only a little remembrance from the past. I have no idea
>> about what happens nowadays.
>> All the best,
>> Giovanni
>>
>>
>>
>>
>> On 5/19/12 10:08 PM, jkennedy at mappi.helsinki.fi wrote:
>>>
>>> Dear Colleagues,
>>>
>>> Speaking of provability logic, does anyone know about this paper?
>>>
>>> A new proof of the fixed-point theorem of provability logic.
>>>
>>> Lisa Reidhaar-Olson
>>> Source: Notre Dame J. Formal Logic Volume 31, Number 1 (1989),
>>> 37-43.
>>>
>>> Do people in provability logic nowadays make use of the result in
>>> any way?
>>>
>>> All the best,
>>>
>>> Juliette Kennedy
>>>
>>>
>>>
>>> Quoting "Richard Heck" <rgheck at brown.edu>:
>>>
>>>> On 05/17/2012 06:19 PM, Craig Smorynski wrote:
>>>>> Aatu Koskensilta quoted me on the issue of who first realised
>>>>> that Löb's Theorem for a theory T is equivalent to the Second
>>>>> Incompleteness Theorem for all finite extensions of T to the
>>>>> effect that I side with Boolos in crediting Kripke.
>>>>> [snip]
>>>>> In any event, there was Boolos's crediting Kripke, which I wrote
>>>>> to him about, feeling it smacked more of hero-worship than
>>>>> scholarship.
>>>>>
>>>> George wasn't really one to worship heroes, though he and Kripke
>>>> were good friends, having first met, I believe, in Oxford in
>>>> 1962-63.
>>>>
>>>> Many years ago now, George and I were having lunch at a restaurant
>>>> in Harvard Square, One Potato, Two Potato, which is now gone.
>>>> George told me that it was at the very table at which Gerald Sacks
>>>> and Burt Dreben then happened to be sitting, not far from us, that
>>>> Kripke had showed him this argument in 1966, and that it was in
>>>> large part that conversation that had sparked his interest in
>>>> provability logic.
>>>>
>>>> Richard Heck
>>>>
>>>>
>>>>
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>>>>
>>>
>>>
>>>
>>
>>
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