Fwd: Supergroup Talk this Week
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Joao Marcos
Apr 28, 2020, 1:58:45 PM4/28/20
to Lista acadêmica brasileira dos profissionais e estudantes da área de LOGICA
---------- Forwarded message ---------
From: Shay Logan <shay.a...@gmail.com>
Date: Tue, Apr 28, 2020, 14:17
Subject: Supergroup Talk this Week
To: Joao Marcos <boto...@gmail.com>
From: Shay Logan <shay.a...@gmail.com>
Date: Tue, Apr 28, 2020, 14:17
Subject: Supergroup Talk this Week
To: Joao Marcos <boto...@gmail.com>
Exciting news! There's yet another logic talk coming up!
Times and dates for these things are confusing. I'll do my best; beginning with the part I'm most certain in:
Date/Time:
Friday, May 1st at 11AM in Melbourne
Friday, May 1st at 3AM in Munich
Thursday, April 30 at 8PM in Manhattan, Kansas
Thursday, April 30 at 10PM in Buenos Aires
Regardless of when or what day it is for you, the event will be the same. And what an event!
Speaker: Tomasz Kowalski (La Trobe)
Title: “Grzegorczyk's proof of undecidability of the theory of concatenation”
Zoom Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09.
Abstract: In his last article, "Undecidability without Arithmetization” (Studia Logica vol.79, no.2, 2005, pp.163-230 https://philpapers.org/rec/GRZUWA-2) Grzegorczyk considers a first-order theory TC in the signature of one binary function and two constants, finitely axiomatised by natural axioms, such that the two-generated model of TC is precisely the set of all nonempty words over a two-letter alphabet. He claims that TC is undecidable.
Grzegorczyk's proof is both interesting and problematic. It is interesting because it proceeds from first principles, using a Goedelian diagonalisation argument, but based intuitively on Grelling "heterological" paradox rather than on the liar. It is problematic, because the notion of computability/decidability it uses is also defined from first principles. We (mostly Yao) proved that everything computable in Grzegorczyk sense is Turing computable, but whether the converse is true is not clear. At least not to us.
I will present Grzegorczyk's proof, or as much of it as Yao and me currently understand. This is work in progress.
Hooray for logic, and we look forward to seeing all of you there!
Shay Allen Logan
Assistant Professor of Philosophy
Kansas State University
Times and dates for these things are confusing. I'll do my best; beginning with the part I'm most certain in:
Date/Time:
Friday, May 1st at 11AM in Melbourne
Friday, May 1st at 3AM in Munich
Thursday, April 30 at 8PM in Manhattan, Kansas
Thursday, April 30 at 10PM in Buenos Aires
Regardless of when or what day it is for you, the event will be the same. And what an event!
Speaker: Tomasz Kowalski (La Trobe)
Title: “Grzegorczyk's proof of undecidability of the theory of concatenation”
Zoom Link: https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09.
Abstract: In his last article, "Undecidability without Arithmetization” (Studia Logica vol.79, no.2, 2005, pp.163-230 https://philpapers.org/rec/GRZUWA-2) Grzegorczyk considers a first-order theory TC in the signature of one binary function and two constants, finitely axiomatised by natural axioms, such that the two-generated model of TC is precisely the set of all nonempty words over a two-letter alphabet. He claims that TC is undecidable.
Grzegorczyk's proof is both interesting and problematic. It is interesting because it proceeds from first principles, using a Goedelian diagonalisation argument, but based intuitively on Grelling "heterological" paradox rather than on the liar. It is problematic, because the notion of computability/decidability it uses is also defined from first principles. We (mostly Yao) proved that everything computable in Grzegorczyk sense is Turing computable, but whether the converse is true is not clear. At least not to us.
I will present Grzegorczyk's proof, or as much of it as Yao and me currently understand. This is work in progress.
Hooray for logic, and we look forward to seeing all of you there!
Shay Allen Logan
Assistant Professor of Philosophy
Kansas State University
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