Comments for Joel David Hamkins
http://jdh.hamkins.org
mathematics and philosophy of the infiniteSat, 28 Mar 2020 06:41:33 +0000
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Comment on Math for eight-year-olds: graph theory for kids! by graph theory for children - Oxford Blog
http://jdh.hamkins.org/math-for-eight-year-olds/#comment-10806
Sat, 28 Mar 2020 06:41:33 +0000http://jdh.hamkins.org/?p=3921#comment-10806[…] to tackle next? One obvious candidate is Hamkin's other pamphlet, on Euler's formula. Then there are Hamiltonian paths and tours. And the concepts of distance and diameter are not […]
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Comment on Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits by graph theory for children - Oxford Blog
http://jdh.hamkins.org/math-for-seven-year-olds-graph-coloring-chromatic-numbers-eulerian-paths/#comment-10805
Sat, 28 Mar 2020 06:41:16 +0000http://jdh.hamkins.org/?p=2869#comment-10805[…] I scrambled to put together a (not used in the end) workshop, based around Joel Hamkin's pamphlet "Graph Coloring and Chromatic Numbers". Helen had no trouble with that, and seems comfortable with chromatic numbers (the smallest number […]
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Comment on Math for kids: fun with orthoprojections! by Marco
http://jdh.hamkins.org/fun-with-orthoprojections/#comment-10804
Fri, 27 Mar 2020 12:10:27 +0000http://jdh.hamkins.org/?p=6627#comment-10804Thank you so much! This is so funny! I don’t have blocks at home, so I draw everything in perspective (with good old pen and paper). I think I’m also going to try this with OpenSCAD ( cube([1,2,4], 0, 0) )…
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Comment on Set-theoretic geology by A tutorial in set-theoretic geology, London 2011 | Joel David Hamkins
http://jdh.hamkins.org/set-theoreticgeology/#comment-10802
Sat, 21 Mar 2020 20:42:49 +0000http://boolesrings.org/hamkins/?p=280#comment-10802[…] Article […]
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Comment on The real numbers are not interpretable in the complex field by Joel David Hamkins
http://jdh.hamkins.org/the-real-numbers-are-not-interpretable-in-the-complex-field/#comment-10800
Wed, 04 Mar 2020 18:45:24 +0000http://jdh.hamkins.org/?p=7407#comment-10800Yes, indeed, one uses the axiom of choice to produce the automorphisms exchanging transcendental elements.
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Comment on The real numbers are not interpretable in the complex field by Ali Enayat
http://jdh.hamkins.org/the-real-numbers-are-not-interpretable-in-the-complex-field/#comment-10799
Wed, 26 Feb 2020 03:30:54 +0000http://jdh.hamkins.org/?p=7407#comment-10799Nice argument. Amusingly, your proof makes an essential use of the axiom of choice since it is known that ZF + “conjugation is the only nontrivial automorphism of the complex field” is consistent (if ZF is consistent).
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Comment on Climb into Cantor's attic by Z
http://jdh.hamkins.org/climb-into-cantors-attic/#comment-10797
Mon, 24 Feb 2020 07:09:28 +0000http://boolesrings.org/hamkins/?p=923#comment-10797Would you please fix the site soon? This is such a good place to learn about large cardinals and set theory, and without it I would have to search through the whole Internet to find what I need. Thanks!
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Comment on Bi-interpretation in weak set theories by Bi-interpretation of weak set theories, Oberwolfach, April 2020 | Joel David Hamkins
http://jdh.hamkins.org/bi-interpretation-in-weak-set-theories/#comment-10796
Sat, 08 Feb 2020 18:04:54 +0000http://jdh.hamkins.org/?p=7360#comment-10796[…] Bi-interpretation in weak set theories […]
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Comment on Win at Nim! The secret mathematical strategy for kids (with challange problems in transfinite Nim for the rest of us) by Joel David Hamkins
http://jdh.hamkins.org/win-at-nim-the-secret-mathematical-strategy/#comment-10795
Sat, 01 Feb 2020 17:16:17 +0000http://jdh.hamkins.org/?p=4222#comment-10795When the piles are height 3 4 5, then the first player can win by playing to 1 4 5. This is a balanced position, to use the terminology of the post, because if you think of 5 as 4+1, then you have two fours and two ones. And there is nothing that the second player can do to avoid losing, if the first player plays the balancing strategy.
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Comment on Win at Nim! The secret mathematical strategy for kids (with challange problems in transfinite Nim for the rest of us) by Anna
http://jdh.hamkins.org/win-at-nim-the-secret-mathematical-strategy/#comment-10794
Fri, 31 Jan 2020 19:13:48 +0000http://jdh.hamkins.org/?p=4222#comment-10794How do you win when the piles are 3,4,5? And what do you do when the other person knows it too?
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Comment on Bi-interpretation in weak set theories by Ali Enayat
http://jdh.hamkins.org/bi-interpretation-in-weak-set-theories/#comment-10793
Fri, 31 Jan 2020 16:06:09 +0000http://jdh.hamkins.org/?p=7360#comment-10793Very beautiful results. The failure of tightness for ZFC without power set, and for Zermelo set theory nicely complement earlier results indicated in the last section of my 2016 paper (referenced in your paper) about the failure of tightness of ZF without the axioms of infinity, and ZF without the foundation axiom. It is also fairly easy to show that tightness fails for ZF without the extensionality axiom, and ZF without the pairing axiom. Did you consider the case of ZF without the union axiom?
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Comment on Bi-interpretation in weak set theories by Bi-interpretation in set theory, Bristol, February 2020 | Joel David Hamkins
http://jdh.hamkins.org/bi-interpretation-in-weak-set-theories/#comment-10792
Wed, 22 Jan 2020 18:25:38 +0000http://jdh.hamkins.org/?p=7360#comment-10792[…] ← Previous […]
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Comment on A new proof of the Barwise extension theorem, without infinitary logic by The $Sigma_1$-definable universal finite sequence | Joel David Hamkins
http://jdh.hamkins.org/a-new-proof-of-the-barwise-extension-theorem/#comment-10791
Tue, 14 Jan 2020 18:44:06 +0000http://jdh.hamkins.org/?p=6765#comment-10791[…] A new proof of the Barwise extension theorem […]
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Comment on Lectures on the philosophy of mathematics, Oxford, Michaelmas term 2019 by Joel David Hamkins
http://jdh.hamkins.org/lectures-on-the-philosophy-of-mathematics-oxford-michaelmas-2019/#comment-10790
Wed, 08 Jan 2020 11:31:33 +0000http://jdh.hamkins.org/?p=7307#comment-10790There is no separate script available, but the book is currently going into production and will be available from MIT Press. I’ll post announcements here when it is available.
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Comment on Lectures on the philosophy of mathematics, Oxford, Michaelmas term 2019 by Klaus Loehnert
http://jdh.hamkins.org/lectures-on-the-philosophy-of-mathematics-oxford-michaelmas-2019/#comment-10789
Wed, 08 Jan 2020 10:43:13 +0000http://jdh.hamkins.org/?p=7307#comment-10789Are there scripts for these lectures, if yes, can I copies of them?
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