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2 changes: 1 addition & 1 deletion _archives/a-game-theoretic-proof-of-fraisse-s-theorem.md
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Expand Up @@ -3,7 +3,7 @@ title: A game-theoretic proof of Fraïssé's Theorem
date: 2011-10-14 04:44:33
permalink: /archives/72/
published: true
categories: [games, model-theory]
topics: [games, model-theory]
tags: [Ehrenfeucht-Fraïssé Games, Fraïssé's Theorem, Game Semantics]
people: [Andrzej Ehrenfeucht, Roland Fraïssé]
---
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2 changes: 1 addition & 1 deletion _archives/a-partition-theorem-for-finite-trees.md
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Expand Up @@ -3,7 +3,7 @@ title: A partition theorem for finite trees
date: 2012-03-03 19:32:37
permalink: /archives/781/
published: true
categories: [combinatorics]
topics: [combinatorics]
tags: [Ramsey Theory, Finite Trees, Ultrametric Spaces]
people: [Alexander Kechris, Daniel McDonald, Frank Ramsey, Lionel Nguyen van Thé, Manuel Rivera, Richard Rado, Steven Gubkin, Stevo Todorcevic, Vladimir Pestov]
---
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Expand Up @@ -3,7 +3,7 @@ title: Arithmetical consequences of the set-theoretic multiverse
date: 2013-02-10 21:33:06
permalink: /archives/1193/
published: true
categories: [mathematical-philosophy, set-theory]
topics: [mathematical-philosophy, set-theory]
tags: [Set-Theoretic Multiverse]
people: [Joel David Hamkins, Victoria Gitman]
---
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2 changes: 1 addition & 1 deletion _archives/back-to-cantor.md
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Expand Up @@ -3,7 +3,7 @@ title: Back to Cantor?
date: 2012-12-28 19:05:07
permalink: /archives/1135/
published: true
categories: [category-theory, mathematical-philosophy, set-theory]
topics: [category-theory, mathematical-philosophy, set-theory]
tags: [ETCS, ZFC]
people: [Bill Lawvere, Ernst Zermelo, Georg Cantor, Tom Leinster]
---
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Expand Up @@ -3,7 +3,7 @@ title: Classically valid theorems of intuitionistic analysis
date: 2011-10-30 18:14:30
permalink: /archives/448/
published: true
categories: [proof-theory, reverse-math]
topics: [proof-theory, reverse-math]
tags: [Intuitionistic Logic, Realizability]
people: [Anne Troelstra, Carl Mummert, Jaap van Oosten, Jeff Hirst, L. E. J. Brouwer]
---
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2 changes: 1 addition & 1 deletion _archives/complete-subspaces-of-a-metric-space.md
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Expand Up @@ -3,7 +3,7 @@ title: Complete subspaces of a metric space
date: 2011-10-14 19:10:57
permalink: /archives/260/
published: true
categories: [topology, set-theory]
topics: [topology, set-theory]
tags: [Cardinal characteristics, Galois-Tukey connections, MathOverflow, Metric spaces]
people: [Andreas Blass, Frank Tall, Peter Vojtáš]
---
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2 changes: 1 addition & 1 deletion _archives/counting-birds.md
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Expand Up @@ -3,7 +3,7 @@ title: Counting Birds...
date: 2011-10-15 17:35:30
permalink: /archives/335/
published: true
categories: [mathematical-philosophy]
topics: [mathematical-philosophy]
tags: [Decidability, MathOverflow]
people: [Jorge Luis Borges, José Figueroa-O'Farrill, Mariano Suárez-Alvarez, Noam Elkies]
---
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2 changes: 1 addition & 1 deletion _archives/diaconescu-s-theorem.md
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Expand Up @@ -3,7 +3,7 @@ title: Diaconescu's Theorem
date: 2012-07-18 16:31:24
permalink: /archives/1031/
published: true
categories: [mathematical-philosophy, set-theory]
topics: [mathematical-philosophy, set-theory]
tags: [Axiom of Choice, Excluded Middle, Intuitionistic Logic]
people: [Per Martin-Löf, Peter Aczel, Radu Diaconescu]
---
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2 changes: 1 addition & 1 deletion _archives/envelope-forcing.md
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Expand Up @@ -3,7 +3,7 @@ title: Envelope forcing
date: 2012-05-06 18:02:01
permalink: /archives/827/
published: true
categories: [combinatorics, computability, independence-proofs, reverse-math]
topics: [combinatorics, computability, independence-proofs, reverse-math]
tags: [Forcing, Ramsey Theory]
people: [Denis Hirschfeldt, Jared Corduan, Reed Solomon, Richard Shore, Rod Downey, Steffen Lempp]
---
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2 changes: 1 addition & 1 deletion _archives/generalized-separation-principles.md
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Expand Up @@ -3,7 +3,7 @@ title: Generalized separation principles
date: 2012-02-26 16:09:16
permalink: /archives/650/
published: true
categories: [computability, reverse-math]
topics: [computability, reverse-math]
tags: [Weak König Lemma]
people: [Carl Jockusch, Doug Cenzer, Itay Neeman, Peter Hinman, Richard Friedberg]
---
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2 changes: 1 addition & 1 deletion _archives/homotopy-type-theory.md
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Expand Up @@ -3,7 +3,7 @@ title: Homotopy Type Theory
date: 2013-06-22 16:41:15
permalink: /archives/1425/
published: true
categories: [mathematical-philosophy, proof-theory, type-theory]
topics: [mathematical-philosophy, proof-theory, type-theory]
tags: [HoTT, Univalence]
---
After a productive year at the Institute for Advanced Study, the Univalent Foundations Program has written a book on [Homotopy Type Theory](http://homotopytypetheory.org/book/) (HoTT). The foreword gives a succinct description of the purpose of this book:
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2 changes: 1 addition & 1 deletion _archives/hott-math-1-elementary-group-theory.md
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Expand Up @@ -3,7 +3,7 @@ title: "HoTT Math 1: Elementary group theory"
date: 2013-06-23 18:00:38
permalink: /archives/1438/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Homotopy Type Theory]
---
This is the first in a series of posts on doing mathematics in Homotopy Type Theory (HoTT). Various conventions and notations are explained in [the preamble]({{ site.baseurl }}{% post_url 2013-06-23-hott-math-series %}); there are no additional prerequisites for this post.
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2 changes: 1 addition & 1 deletion _archives/hott-math-2-more-on-equational-logic.md
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Expand Up @@ -3,7 +3,7 @@ title: "HoTT Math 2: More on equational logic"
date: 2013-07-14 16:03:09
permalink: /archives/1476/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Equational Logic, Homotopy Type Theory, Universal Algebra]
people: [Garrett Birkhoff]
---
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2 changes: 1 addition & 1 deletion _archives/hott-math-3-unit-group-of-a-ring.md
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Expand Up @@ -3,7 +3,7 @@ title: "HoTT Math 3: Unit group of a ring"
date: 2013-07-14 20:30:01
permalink: /archives/1488/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Homotopy Type Theory]
---
In this installment of [HoTT Math]({{ site.baseurl }}{% post_url 2013-06-23-hott-math-series %}), we are taking one more step toward elementary field theory by exploring the unit group of a ring.
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2 changes: 1 addition & 1 deletion _archives/hott-math-4-local-rings-and-fields.md
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Expand Up @@ -3,7 +3,7 @@ title: "HoTT Math 4: Local rings and fields"
date: 2013-12-10 01:13:28
permalink: /archives/1517/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Homotopy Type Theory]
---
It's been a while since the last edition of [HoTT Math]({{ "archives/1448" | relative_url }}). Fall is always very busy for me and I've been composing this installment one $$\varepsilon$$ at a time... We are finally arriving at our destination: fields!
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3 changes: 2 additions & 1 deletion _archives/on-a-theorem-of-mycielski-and-taylor.md
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Expand Up @@ -3,10 +3,11 @@ title: On a theorem of Mycielski and Taylor
date: 2011-11-06 19:28:03
permalink: /archives/503/
published: true
categories: [combinatorics, set-theory]
topics: [combinatorics, set-theory]
tags: [Cardinal Characteristics, Independent Sets, Polish Spaces, Ramsey Theory]
people: [Alan Taylor, Andreas Blass, Fred Galvin, Jan Mycielski, Rafał Filipów, Tomasz Natkaniec]
---

{% include t.cite _='Myc64n' %} proved a wonderful theorem about independent sets in Polish spaces. He showed that if $$X$$ is an uncountable Polish space and $$R_n$$ is a meager subset of $$X^n$$ for each $$n \geq 1$$, then there is a perfect set $$Z \subseteq X$$ such that $$(z_1,\dots,z_n) \notin R_n$$ whenever $$z_1,\dots,z_n$$ are distinct elements of $$Z$$. In other words, $$Z$$ is $$R_n$$-independent for each $$n \geq 1$$. This is a wonderfully general theorem that has a multitude of applications.

One of my favorite theorems where Mycielski's Theorem comes in handy is a remarkable partition theorem due to Fred Galvin.
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2 changes: 1 addition & 1 deletion _archives/on-computing-complex-square-roots.md
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Expand Up @@ -3,7 +3,7 @@ title: On computing complex square roots
date: 2011-10-22 16:15:34
permalink: /archives/377/
published: true
categories: [computability, reverse-math]
topics: [computability, reverse-math]
---
What could possibly be interesting about complex square roots? That's what I thought until very recently when I realized that complex square roots are significantly more difficult to compute than real square roots. Let me explain why by putting you in a context where you need to teach students how to compute complex square roots...

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2 changes: 1 addition & 1 deletion _archives/on-the-structure-of-universes-in-hott.md
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Expand Up @@ -3,7 +3,7 @@ title: On the structure of universes in HoTT
date: 2014-01-17 03:40:20
permalink: /archives/1532/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Homotopy Type Theory]
people: [Alexander Kuklev, Andrej Bauer, Mike Shulman]
---
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2 changes: 1 addition & 1 deletion _archives/paris-harrington-and-typing.md
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Expand Up @@ -3,7 +3,7 @@ title: Paris-Harrington and Typing
date: 2011-10-14 04:44:34
permalink: /archives/107/
published: true
categories: [independence-proofs, set-theory]
topics: [independence-proofs, set-theory]
tags: [New Foundations, Paris-Harrington Theorem, Peano Arithmetic]
people: [Harvey Friedman, Thomas Forster]
---
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2 changes: 1 addition & 1 deletion _archives/santa-exists.md
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Expand Up @@ -3,7 +3,7 @@ title: Santa Exists!
date: 2011-10-15 15:38:37
permalink: /archives/317/
published: true
categories: [mathematical-philosophy, proof-theory, set-theory]
topics: [mathematical-philosophy, proof-theory, set-theory]
tags: [Intuitionistic Logic, Minimal Logic, Russell's Paradox, Self-Reference]
people: [Bertrand Russell, Haskell Curry]
---
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2 changes: 1 addition & 1 deletion _archives/scheming-schemes.md
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Expand Up @@ -3,7 +3,7 @@ title: Scheming schemes...
date: 2012-08-15 20:22:16
permalink: /archives/1080/
published: true
categories: [model-theory, reverse-math, set-theory]
topics: [model-theory, reverse-math, set-theory]
tags: [MathOverflow, Reflection Principles]
people: [Joel David Hamkins]
---
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2 changes: 1 addition & 1 deletion _archives/some-cardinal-arithmetic.md
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Expand Up @@ -3,7 +3,7 @@ title: Some Cardinal Arithmetic
date: 2014-11-09 20:09:55
permalink: /archives/1593/
published: true
categories: [combinatorics, set-theory]
topics: [combinatorics, set-theory]
tags: [Axiom of Choice, Cardinal Arithmetic]
people: [Asaf Karagila, Harvey Friedman, Peter Krautzberger]
---
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2 changes: 1 addition & 1 deletion _archives/stationary-strategies-in-choquet-games.md
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Expand Up @@ -3,7 +3,7 @@ title: Stationary strategies in Choquet games
date: 2011-10-14 04:46:41
permalink: /archives/38/
published: true
categories: [topology, games]
topics: [topology, games]
tags: [Choquet game, MF spaces]
people: [Carl Mummert, Frank Stephan]
---
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2 changes: 1 addition & 1 deletion _archives/subposets-of-small-dimension.md
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Expand Up @@ -3,7 +3,7 @@ title: Subposets of small dimension
date: 2012-02-18 16:18:28
permalink: /archives/656/
published: true
categories: [combinatorics, reverse-math, set-theory]
topics: [combinatorics, reverse-math, set-theory]
tags: [Dushnik-Miller Dimension, MathOverflow, Open Problems, Posets, Ramsey Theory]
people: [Denis Hirschfeldt, Justin Tatch Moore, Richard Shore, Tom Goodwillie, Wacław Sierpiński]
---
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2 changes: 1 addition & 1 deletion _archives/super-hott.md
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Expand Up @@ -3,7 +3,7 @@ title: Super HoTT
date: 2014-01-19 20:31:52
permalink: /archives/1543/
published: true
categories: [type-theory]
topics: [type-theory]
tags: [Homotopy Type Theory]
people: [Andrej Bauer, Erik Palmgren]
---
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2 changes: 1 addition & 1 deletion _archives/towsner-s-stable-forcing.md
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Expand Up @@ -3,7 +3,7 @@ title: Towsner's stable forcing
date: 2013-02-08 15:09:36
permalink: /archives/1203/
published: true
categories: [independence-proofs, reverse-math]
topics: [independence-proofs, reverse-math]
tags: [Forcing, Second-Order Arithmetic]
people: [Henry Towsner, Ted Slaman]
---
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2 changes: 1 addition & 1 deletion _archives/uncountable-perfect-graphs.md
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Expand Up @@ -3,7 +3,7 @@ title: Uncountable perfect graphs
date: 2011-11-06 15:03:58
permalink: /archives/431/
published: true
categories: [combinatorics, set-theory]
topics: [combinatorics, set-theory]
tags: [Chordal Graphs, Comparability Graphs, Interval Graphs, Perfect Graphs]
people: [Claude Berge, Fred Galvin, László Lovász, Maria Chudnovsky, Misha Perles, Neil Robertson, Paul Seymour, Richard Rado, Robin Thomas, Ron Aharoni, Stan Wagon, Stevo Todorcevic, Uri Abraham]
---
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2 changes: 1 addition & 1 deletion _archives/what-is-combinatorial-set-theory.md
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Expand Up @@ -3,7 +3,7 @@ title: What is combinatorial set theory?
date: 2013-05-11 14:51:55
permalink: /archives/1394/
published: true
categories: [combinatorics, set-theory]
topics: [combinatorics, set-theory]
tags: [Combinatorial Set Theory]
people: [Jim Baumgartner, Ken Kunen, Neil Williams, Thomas Jech]
---
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20 changes: 17 additions & 3 deletions _config.yml
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Expand Up @@ -32,14 +32,28 @@ defaults:
section: archives
layout: post

# Topics
topic_map:
combinatorics: Combinatorics
computability: Computability Theory
independence-proofs: Forcing and Independence Proofs
games: Mathematical Games
mathematical-philosophy: Mathematical Philosophy
model-theory: Model Theory
proof-theory: Proof Theory
reverse-math: Reverse Mathematics
set-theory: Set Theory
topology: Topology
type-theory: Type Theory

# Sorting modes
sorting:
- name: category
url: /archives/category.html
- name: date
url: /archives/date.html
- name: title
url: /archives/title.html
- name: topic
url: /archives/topic.html

# Navigation
page_nav:
Expand All @@ -51,7 +65,7 @@ page_nav:
url: /papers/index.html
- title: "Posts"
section: archives
url: /archives/category.html
url: /archives/topic.html
- title: "News"
section: news
url: /news/index.html
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10 changes: 10 additions & 0 deletions _layouts/post.html
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@@ -1,8 +1,18 @@
---
layout: default
---
{% if page.topics %}
<ul id="topics" class="hlist">
Topics
{% for t in page.topics %}
<li><a href="{{ '/archives/topic.html#' | append: t | relative_url }}">{{ site.topic_map[t] }}</a></li>
{% endfor %}
</ul>
<hr />
{% endif %}
<h2>{{ page.title }}</h2>


{{ content }}

{% include license.html %}
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41 changes: 0 additions & 41 deletions archives-by-category.html

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19 changes: 19 additions & 0 deletions archives-by-topic.html
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@@ -0,0 +1,19 @@
---
title: Posts
layout: list
mode: topic
section: archives
permalink: /archives/topic.html
---
{% for _ in site.topic_map %}
{% assign t = _[0] %}
<h4 id="{{ t }}">{{ site.topic_map[t] }}</h4>
<ul class="listing">
{% assign posts = site.archives | where_exp: "p", "p.topics contains t" %}
{% for p in posts %}
<li>
<a href="{{ p.url | relative_url }}">{{ p.title }}</a>
</li>
{% endfor %}
</ul>
{% endfor %}
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