#PanoramaOfLogic

Nondefinability and higher definability Nondefinability, definable sets and relations, and implicit definability

Please enjoy my essay on nondefinabilty. #InfinitelyMore #PanoramaOfLogic
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The lattice of all sets of natural numbers Let us explore the vast and densely populated expanses of the lattice of all sets of natural numbers—the power set lattice ⟨P(ℕ),⊆⟩—seeking monsters and wild suborders inhabiting this land.

What structure can you find in the lattice of all sets of natural numbers? Is there a chain ordered like the real numbers? An uncountable antichain of incomparability? Which orders embed into this lattice? #InfinitelyMore #PanoramaOfLogic
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Epistemic logic and the problem of common knowledge With the two generals, Cheryl's birthday, hidden surprises, blue-eyed islanders, pirate treasure division, philosopher's ruling council, coordination paradox, Fitch's paradox, Cheryl's rational gifts

Time for epistemic logic puzzles!
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We are discussing these next week in my Core Seminar in Philosophy, Science, and Mathematics.

Infinitely More | Joel David Hamkins | Substack The mathematics and philosophy of the infinite. Click to read Infinitely More, by Joel David Hamkins, a Substack publication with thousands of subscribers.

See my series of essays on the concept of interpretability for models and theories in first-order logic.
www.infinitelymore.xyz/t/interpreta... #InfinitelyMore #PanoramaOfLogic

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 of the host theory.

Interpretability of theories.
This week's installment of A Panorama of Logic.
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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.

Enjoy another post in my recent series on interpretation.
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 translation.

I am making a series of posts on interpretability in mathematics, which occurs when we can simulate a copy of one mathematical structure within another. This week's post is on the resulting interpretation translation.
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Interpretability We can often simulate one model inside another, providing a translation of meaning from the first realm to the second.

Please enjoy this week's installment from A Panorama of Logic, the first of a series of posts I shall make on the topic of interpretability, by which we simulate a copy of one mathematical structure within another.
infinitelymore.xyz/p/interpreta...
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