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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Fri, 5 Jul 2002 19:54:27 +0200

Hi Wei Dai,

About books. Concerning the provability logics I always mentionned

the Boolos 1993 (or even his lovely lighter Boolos 1979), but I would

like to mention also the book "Self-reference and modal logic" by

Smorynski. The only problem is its very little caracters; I should go

to the occulist! :0 But he has a nice chapter on the algebraic models

of the provability logic: the so called diagonalisable algebras and

fixed point algebras. As you know the Z logics I got are so weak that

they loose (like G*) Kripke semantics or even Scott-Montague

(sort of topological) semantics. So we need some algebraic move.

Note that the G/G* story *begun* with those diagonalisable algebra

through the work of Magari (Italy).

But, perhaps more importantly at this stage I must recall the book

"Mathematics of Modality" by Robert Goldblatt. It contains fundamental

papers on which my "quantum" derivation relies. I mentionned it a lot

some time ago.

And now that I speak about Goldblatt, because of Tim May who dares

to refer to algebra, category and topos! I want mention that Goldblatt

did wrote an excellent introduction to Toposes: "Topoi". (One of the big

problem in topos theory is which plural chose for the word "topos". There

are two schools: topoi (like Goldblatt), and toposes (like Bar and

Wells). :)

Goldblatt book on topoi has been heavily attacked by "pure categorically

minded algebraist like Johnstone for exemple, because there is a remnant

smell of set theory in topoi. That is true, but that really help for an

introduction. So, if you want to be introduced to the topos theory,

Goldblatt Topoi, North Holland editor 19?(I will look at home) is

perhaps the one.

-Bruno

PS I get your questions. I will think a little bit before answering.

Thanks to Tim for Egan's exerp.

Received on Fri Jul 05 2002 - 10:51:44 PDT

Date: Fri, 5 Jul 2002 19:54:27 +0200

Hi Wei Dai,

About books. Concerning the provability logics I always mentionned

the Boolos 1993 (or even his lovely lighter Boolos 1979), but I would

like to mention also the book "Self-reference and modal logic" by

Smorynski. The only problem is its very little caracters; I should go

to the occulist! :0 But he has a nice chapter on the algebraic models

of the provability logic: the so called diagonalisable algebras and

fixed point algebras. As you know the Z logics I got are so weak that

they loose (like G*) Kripke semantics or even Scott-Montague

(sort of topological) semantics. So we need some algebraic move.

Note that the G/G* story *begun* with those diagonalisable algebra

through the work of Magari (Italy).

But, perhaps more importantly at this stage I must recall the book

"Mathematics of Modality" by Robert Goldblatt. It contains fundamental

papers on which my "quantum" derivation relies. I mentionned it a lot

some time ago.

And now that I speak about Goldblatt, because of Tim May who dares

to refer to algebra, category and topos! I want mention that Goldblatt

did wrote an excellent introduction to Toposes: "Topoi". (One of the big

problem in topos theory is which plural chose for the word "topos". There

are two schools: topoi (like Goldblatt), and toposes (like Bar and

Wells). :)

Goldblatt book on topoi has been heavily attacked by "pure categorically

minded algebraist like Johnstone for exemple, because there is a remnant

smell of set theory in topoi. That is true, but that really help for an

introduction. So, if you want to be introduced to the topos theory,

Goldblatt Topoi, North Holland editor 19?(I will look at home) is

perhaps the one.

-Bruno

PS I get your questions. I will think a little bit before answering.

Thanks to Tim for Egan's exerp.

Received on Fri Jul 05 2002 - 10:51:44 PDT

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