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_posts/2022-05-17-e-pluribus-unum.html

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Athena sprang forth full grown from the head of Zeus. Newton/Leibniz created Calculus. Galois created Galois Theory. Cantor created Set Theory. Boole created Boolean Algebra.</p>
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<p>
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But Models of Peano Arithmetic doesn’t have a dramatic origin myth like that and took some 100 years to emerge as a discipline in itself - from Dedekind’s Second Order Axioms for Arithmetic (1863), through Frege’s Begriffsschrift (1879) and First Order Logic, through Godel’s Completeness and Incompleteness Theorems, through Skolem’s elegant construction of a non-standard model, through the War and après-guerre and on into the 1970s where the subject at last emerges as a discipline in itself. We’ll discuss the convergence of people and ideas from diverse fields like Model Theory, Set Theory, Recursion Theory, Proof Theory, Complexity Theory, … that led to the field we know and love today.</p>
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<p><strong><a href=''>Video</a></strong></p>
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<p><strong><a href='https://www.youtube.com/watch?v=lBDls5Hv6qk'>Video</a></strong></p>
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<p><strong><a href='/files/McAloonSlides052022.pdf'>Slides</a></strong></p>
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​"
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excerpt_separator: <!--more-->
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talk: yes

_posts/2022-05-24-the-winding-road-to-mathematical-independence-results-for-pa.html

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speaker_first: Laurence
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speaker_last: Kirby
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speaker_website:
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affiliation: Brooklyn College
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affiliation: Baruch College
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abstract: "
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<p>
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Advances in understanding the incompleteness of PA in the 1970s and 80s
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---
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layout: talk
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title: MOPA
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talk_title: Another quantifier-elimination result in arithmetic under negated induction
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categories: MOPA
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date: 2022-05-31
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semester: spring-2020
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speaker_first: Tin Lok
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speaker_last: Wong
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speaker_website: "https://blog.nus.edu.sg/matwong/"
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affiliation: National University of Singapore
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abstract: "
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<p>
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In a paper published in 1990, Kossak showed that all countable models of $&#92;Sigma_n$ collection where $&#92;Sigma_n$ induction fails have continuum-many automorphisms. We extract from his proof a(nother) quantifier-elimination result. This gives new information about pigeonhole principles and expansions to second-order models. The work is joint with David Belanger, CT Chong, Wei Li, and Yue Yang at the National University of Singapore.
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</p>
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<p><strong><a href=''>Video</a></strong></p>
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​"
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excerpt_separator: <!--more-->
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talk: yes
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note: "<strong>8:00pm</strong> NY time<br>
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<font color='red' size='3'><strong>Virtual</strong> </font>(email <a href='mailto:vgitman@nylogic.org'>Victoria Gitman</a> for meeting id)"
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_posts/2022-05-31-mopa-tba.html

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files/McAloonSlides052022.pdf

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