In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical.
The arithmetical hierarchy assigns classifications to the formulas in the language of first-order arithmetic. The classifications are denoted and for natural numbers n (including 0). The Greek letters here are lightface symbols, which indicates that the formulas do not contain set parameters.
A presentation for my CS 139 class on the Arithmetic Hierarchy
published: 06 May 2023
Math 557 – Arithmetic Formulas
Math 557, Mathematical Logic, Penn State, Spring 2021; Week 13, Video #2
published: 12 Apr 2021
Chomsky Hierarchy - Computerphile
Uncomputable through to finite state - Professor Brailsford explains Chomsky's hierarchy.
Turing and the Halting Problem: https://youtu.be/macM_MtS_w4
"Most Difficult Program" - Ackermann Function: http://youtu.be/i7sm9dzFtEI
Busy Beaver Turing Machines: https://youtu.be/CE8UhcyJS0I
Finite State Automata: https://youtu.be/vhiiia1_hC4
Reverse Polish & The Stack: https://youtu.be/7ha78yWRDlE
Programming in Postscript: https://youtu.be/S_NXz7I5dQc
Professor Brailsford's Notes: http://bit.ly/computerphile_Chomsky
Professor Brailsford's t-shirt kindly supplied by Peleg Bar Sapir
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphil...
published: 13 Jan 2016
What does arithmetical hierarchy mean?
What does arithmetical hierarchy mean?
A spoken definition of arithmetical hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetical_hierarchy
Text to Speech powered by TTS-API.COM
published: 28 Sep 2015
Arithmetical hierarchy
If you find our videos helpful you can support us by buying something from amazon.
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Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.Any set that receives a classification is called arithmetical.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=iiq0WmsK7j8
published: 22 Jan 2016
What does arithmetic hierarchy mean?
What does arithmetic hierarchy mean?
A spoken definition of arithmetic hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetic_hierarchy
published: 21 Aug 2018
Computational complexity, arithmetical hierarchy and mathematical fuzzy logic - Petr Hájek
The lecture of Petr Hájek, 'Computational complexity, arithmetical hierarchy and mathematical fuzzy logic', presented at the "Trends in Logic IX" conference - Church's Thesis: Logic, Mind and Nature, 3-5 June 2011, Kraków, Poland.
The conference was co-organized by Copernicus Center for Interdisciplinary Studies.
Photos: http://www.adamwalanus.pl/2011/cc1605.html
published: 20 Nov 2011
QIP 2022 | Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy (Hamoon Mousavi)
Title: Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy
Authors: Hamoon Mousavi, Seyed Sajjad Nezhadi and Henry Yuen
published: 30 Mar 2022
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Helpful? Please support me on Patreon: https://www.patreon.com/roelvandepaar
With thanks & praise to God, and with thanks to the many people who have made this project possible! | Content (except music & images) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing | Music: https://www.bensound.com/licensing | Images: https://stocksnap.io/license & others | With thanks to user Yuval Filmus (cs.stackexchange.com/users/683), user hh vh (cs.stackexchange.com/users/111597), and the Stack Exchange Network (cs.stackexchange.com/questions/122001). Trademarks are property of their respective owners. Disclaimer: All information is provided "AS IS" without warranty of any kind. You are responsible for ...
Uncomputable through to finite state - Professor Brailsford explains Chomsky's hierarchy.
Turing and the Halting Problem: https://youtu.be/macM_MtS_w4
"Most Di...
Uncomputable through to finite state - Professor Brailsford explains Chomsky's hierarchy.
Turing and the Halting Problem: https://youtu.be/macM_MtS_w4
"Most Difficult Program" - Ackermann Function: http://youtu.be/i7sm9dzFtEI
Busy Beaver Turing Machines: https://youtu.be/CE8UhcyJS0I
Finite State Automata: https://youtu.be/vhiiia1_hC4
Reverse Polish & The Stack: https://youtu.be/7ha78yWRDlE
Programming in Postscript: https://youtu.be/S_NXz7I5dQc
Professor Brailsford's Notes: http://bit.ly/computerphile_Chomsky
Professor Brailsford's t-shirt kindly supplied by Peleg Bar Sapir
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
Uncomputable through to finite state - Professor Brailsford explains Chomsky's hierarchy.
Turing and the Halting Problem: https://youtu.be/macM_MtS_w4
"Most Difficult Program" - Ackermann Function: http://youtu.be/i7sm9dzFtEI
Busy Beaver Turing Machines: https://youtu.be/CE8UhcyJS0I
Finite State Automata: https://youtu.be/vhiiia1_hC4
Reverse Polish & The Stack: https://youtu.be/7ha78yWRDlE
Programming in Postscript: https://youtu.be/S_NXz7I5dQc
Professor Brailsford's Notes: http://bit.ly/computerphile_Chomsky
Professor Brailsford's t-shirt kindly supplied by Peleg Bar Sapir
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
What does arithmetical hierarchy mean?
A spoken definition of arithmetical hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro M...
What does arithmetical hierarchy mean?
A spoken definition of arithmetical hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetical_hierarchy
Text to Speech powered by TTS-API.COM
What does arithmetical hierarchy mean?
A spoken definition of arithmetical hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetical_hierarchy
Text to Speech powered by TTS-API.COM
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Arithmetical hierarchy
In mathem...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.Any set that receives a classification is called arithmetical.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=iiq0WmsK7j8
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.Any set that receives a classification is called arithmetical.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=iiq0WmsK7j8
What does arithmetic hierarchy mean?
A spoken definition of arithmetic hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music...
What does arithmetic hierarchy mean?
A spoken definition of arithmetic hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetic_hierarchy
What does arithmetic hierarchy mean?
A spoken definition of arithmetic hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetic_hierarchy
The lecture of Petr Hájek, 'Computational complexity, arithmetical hierarchy and mathematical fuzzy logic', presented at the "Trends in Logic IX" conference - C...
The lecture of Petr Hájek, 'Computational complexity, arithmetical hierarchy and mathematical fuzzy logic', presented at the "Trends in Logic IX" conference - Church's Thesis: Logic, Mind and Nature, 3-5 June 2011, Kraków, Poland.
The conference was co-organized by Copernicus Center for Interdisciplinary Studies.
Photos: http://www.adamwalanus.pl/2011/cc1605.html
The lecture of Petr Hájek, 'Computational complexity, arithmetical hierarchy and mathematical fuzzy logic', presented at the "Trends in Logic IX" conference - Church's Thesis: Logic, Mind and Nature, 3-5 June 2011, Kraków, Poland.
The conference was co-organized by Copernicus Center for Interdisciplinary Studies.
Photos: http://www.adamwalanus.pl/2011/cc1605.html
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Helpful? Please support me on Patreon: https://www.patreon.com/roelvandepaar
...
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Helpful? Please support me on Patreon: https://www.patreon.com/roelvandepaar
With thanks & praise to God, and with thanks to the many people who have made this project possible! | Content (except music & images) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing | Music: https://www.bensound.com/licensing | Images: https://stocksnap.io/license & others | With thanks to user Yuval Filmus (cs.stackexchange.com/users/683), user hh vh (cs.stackexchange.com/users/111597), and the Stack Exchange Network (cs.stackexchange.com/questions/122001). Trademarks are property of their respective owners. Disclaimer: All information is provided "AS IS" without warranty of any kind. You are responsible for your own actions. Please contact me if anything is amiss at Roel D.OT VandePaar A.T gmail.com
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Helpful? Please support me on Patreon: https://www.patreon.com/roelvandepaar
With thanks & praise to God, and with thanks to the many people who have made this project possible! | Content (except music & images) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing | Music: https://www.bensound.com/licensing | Images: https://stocksnap.io/license & others | With thanks to user Yuval Filmus (cs.stackexchange.com/users/683), user hh vh (cs.stackexchange.com/users/111597), and the Stack Exchange Network (cs.stackexchange.com/questions/122001). Trademarks are property of their respective owners. Disclaimer: All information is provided "AS IS" without warranty of any kind. You are responsible for your own actions. Please contact me if anything is amiss at Roel D.OT VandePaar A.T gmail.com
Uncomputable through to finite state - Professor Brailsford explains Chomsky's hierarchy.
Turing and the Halting Problem: https://youtu.be/macM_MtS_w4
"Most Difficult Program" - Ackermann Function: http://youtu.be/i7sm9dzFtEI
Busy Beaver Turing Machines: https://youtu.be/CE8UhcyJS0I
Finite State Automata: https://youtu.be/vhiiia1_hC4
Reverse Polish & The Stack: https://youtu.be/7ha78yWRDlE
Programming in Postscript: https://youtu.be/S_NXz7I5dQc
Professor Brailsford's Notes: http://bit.ly/computerphile_Chomsky
Professor Brailsford's t-shirt kindly supplied by Peleg Bar Sapir
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com
What does arithmetical hierarchy mean?
A spoken definition of arithmetical hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetical_hierarchy
Text to Speech powered by TTS-API.COM
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.Any set that receives a classification is called arithmetical.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=iiq0WmsK7j8
What does arithmetic hierarchy mean?
A spoken definition of arithmetic hierarchy.
Intro Sound:
Typewriter - Tamskp
Licensed under CC:BA 3.0
Outro Music:
Groove Groove - Kevin MacLeod (incompetech.com)
Licensed under CC:BA 3.0
Intro/Outro Photo:
The best days are not planned - Marcus Hansson
Licensed under CC-BY-2.0
Book Image:
Open Book template PSD - DougitDesign
Licensed under CC:BA 3.0
Text derived from:
http://en.wiktionary.org/wiki/arithmetic_hierarchy
The lecture of Petr Hájek, 'Computational complexity, arithmetical hierarchy and mathematical fuzzy logic', presented at the "Trends in Logic IX" conference - Church's Thesis: Logic, Mind and Nature, 3-5 June 2011, Kraków, Poland.
The conference was co-organized by Copernicus Center for Interdisciplinary Studies.
Photos: http://www.adamwalanus.pl/2011/cc1605.html
Computer Science: Arithmetical Hierarchy, show $Sigma_1$ is Turing recognizable
Helpful? Please support me on Patreon: https://www.patreon.com/roelvandepaar
With thanks & praise to God, and with thanks to the many people who have made this project possible! | Content (except music & images) licensed under CC BY-SA https://meta.stackexchange.com/help/licensing | Music: https://www.bensound.com/licensing | Images: https://stocksnap.io/license & others | With thanks to user Yuval Filmus (cs.stackexchange.com/users/683), user hh vh (cs.stackexchange.com/users/111597), and the Stack Exchange Network (cs.stackexchange.com/questions/122001). Trademarks are property of their respective owners. Disclaimer: All information is provided "AS IS" without warranty of any kind. You are responsible for your own actions. Please contact me if anything is amiss at Roel D.OT VandePaar A.T gmail.com
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical.
The arithmetical hierarchy assigns classifications to the formulas in the language of first-order arithmetic. The classifications are denoted and for natural numbers n (including 0). The Greek letters here are lightface symbols, which indicates that the formulas do not contain set parameters.