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Interpretability of theories
We interpret one theory in another when we can translate all the concepts and structures of the first theory into the language and structural resources…
Jan 11
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Joel David Hamkins
7
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Interpretability of theories
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3
The zigzag theorem
A selection from Proof and the Art of Mathematics
Jan 4
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Joel David Hamkins
13
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The zigzag theorem
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December 2024
Take my Infinity final exam!
How well can you answer the questions on the final exam for my Infinity course?
Dec 21, 2024
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Joel David Hamkins
14
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Take my Infinity final exam!
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15
Mutual and bi-interpretation of models
Enjoy this installment from A Panorama of Logic, an introduction to topics in logic for philosophers, mathematicians, and computer scientists.
Dec 14, 2024
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Joel David Hamkins
7
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Mutual and bi-interpretation of models
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The interpretation translation
We give a precise account of what it means to interpret one mathematical structure in another, and show how this leads to the interpretation…
Dec 7, 2024
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Joel David Hamkins
5
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The interpretation translation
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November 2024
Interpretability
We can often simulate one model inside another, providing a translation of meaning from the first realm to the second.
Nov 30, 2024
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Joel David Hamkins
11
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Interpretability
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Permutations and combinations
A selection from Proof and the Art of Mathematics
Nov 17, 2024
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Joel David Hamkins
8
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Permutations and combinations
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What is the essential structure of the complex numbers?
I discuss several commonly held perspectives on the complex numbers and explore how their differences engage with several aspects of structuralism in…
Nov 10, 2024
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Joel David Hamkins
15
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What is the essential structure of the complex numbers?
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October 2024
Representing integers as a sum
A quick selection from Proof and the Art of Mathematics
Oct 27, 2024
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Joel David Hamkins
3
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Representing integers as a sum
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2
Recursive Chess
What is the game of recursive chess?
Oct 19, 2024
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Joel David Hamkins
5
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Recursive Chess
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4
Finite and transfinite variations of Escape!
Can you win the Escape! game with transfinite play? Can you win a finite-board variation of the game?
Oct 10, 2024
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Joel David Hamkins
7
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Finite and transfinite variations of Escape!
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Escape!
A selection from Proof and the Art of Mathematics
Oct 2, 2024
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Joel David Hamkins
10
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Escape!
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