User Joel David Hamkins

25 votes

Non-definability of graph 3-colorability in first-order logic

answered Jul 7, 2023 at 20:58

25 votes

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Universal order type

answered Mar 6, 2011 at 20:58

25 votes

Axiom of choice and non-measurable set

answered Aug 28, 2011 at 17:55

25 votes

Is it possible to partition $\mathbb R^3$ into unit circles?

answered Jun 18, 2010 at 19:07

25 votes

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Non-computable but easily described arithmetical functions

answered Jun 23, 2010 at 12:37

25 votes

How do you approach your child's math education?

answered Mar 31, 2010 at 16:33

25 votes

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Is there a known way to formalise notion that certain theorems are essential ones?

answered Mar 14, 2010 at 5:11

25 votes

The Importance of ZF

answered Nov 20, 2009 at 22:09

25 votes

Do sets with positive Lebesgue measure have same cardinality as R?

answered Dec 15, 2009 at 19:06

25 votes

Term for "uncheckable constructions"

answered Nov 16, 2014 at 21:50

25 votes

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Can We Decide Whether Small Computer Programs Halt?

answered Dec 29, 2013 at 23:33

25 votes

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Is deciding whether a Turing machine provably runs forever equivalent to the halting problem?

answered May 22, 2013 at 3:16

24 votes

Nearly all math classes are lecture+problem set based; this seems particularly true at the graduate level. What are some concrete examples of techniques other than the "standard math class" used at the Graduate level?

answered Jun 13, 2013 at 15:00

24 votes

Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice?

answered Aug 24, 2012 at 21:33

24 votes

Logic in mathematics and philosophy

answered Jan 30, 2014 at 19:14

24 votes

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Is Dependent Choice all we really need?

answered Dec 9, 2009 at 21:28

24 votes

Accepted

Basis of l^infinity

answered Dec 12, 2009 at 3:25

24 votes

Bourbaki's epsilon-calculus notation

answered Feb 6, 2010 at 4:02

24 votes

What part do arguments from authority play in mathematical reasoning?

answered Jun 14, 2010 at 4:16

24 votes

Kuratowski's definition of ordered pairs

answered Apr 24, 2011 at 3:12

24 votes

Accepted

Which recursively-defined predicates can be expressed in Presburger Arithmetic?

answered Sep 5, 2010 at 11:46

24 votes

Does every set admit a ring structure or a field structure?

answered Jul 11, 2023 at 17:45

24 votes

Accepted

Definable set in ZF that cannot be proved to be Borel

answered Nov 22, 2022 at 14:39

24 votes

Is platonism regarding arithmetic consistent with the multiverse view in set theory?

answered Jan 22, 2016 at 18:57

24 votes

Accepted

What is the relationship between Turing Machines and Gödel's Incompleteness Theorem?

answered Dec 30, 2015 at 13:45

24 votes

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Large categories vs. $\mathrm{U}$-categories: why is the loss of category-theoretic information inessential?

answered Aug 27, 2017 at 13:42

23 votes

Can $L$ be thin?

answered Oct 6, 2015 at 20:05

23 votes

Accepted

Are the categories of sets, abelian groups, and commutative rings unique?

answered Oct 26, 2022 at 0:05

23 votes

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An infinite game possibly due to Ernst Specker

answered Aug 6, 2021 at 11:12

23 votes

What's the bijection between reals and infinite sequences of integers?

answered May 20, 2021 at 19:22

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1,913 Answers

Non-definability of graph 3-colorability in first-order logic

Universal order type

Axiom of choice and non-measurable set

Is it possible to partition $\mathbb R^3$ into unit circles?

Non-computable but easily described arithmetical functions

How do you approach your child's math education?

Is there a known way to formalise notion that certain theorems are essential ones?

The Importance of ZF

Do sets with positive Lebesgue measure have same cardinality as R?

Term for "uncheckable constructions"

Can We Decide Whether Small Computer Programs Halt?

Is deciding whether a Turing machine provably runs forever equivalent to the halting problem?

Nearly all math classes are lecture+problem set based; this seems particularly true at the graduate level. What are some concrete examples of techniques other than the "standard math class" used at the Graduate level?

Does $2^X=2^Y\Rightarrow |X|=|Y|$ imply the axiom of choice?

Logic in mathematics and philosophy

Is Dependent Choice all we really need?

Basis of l^infinity

Bourbaki's epsilon-calculus notation

What part do arguments from authority play in mathematical reasoning?

Kuratowski's definition of ordered pairs

Which recursively-defined predicates can be expressed in Presburger Arithmetic?

Does every set admit a ring structure or a field structure?

Definable set in ZF that cannot be proved to be Borel

Is platonism regarding arithmetic consistent with the multiverse view in set theory?

What is the relationship between Turing Machines and Gödel's Incompleteness Theorem?

Large categories vs. $\mathrm{U}$-categories: why is the loss of category-theoretic information inessential?

Can $L$ be thin?

Are the categories of sets, abelian groups, and commutative rings unique?

An infinite game possibly due to Ernst Specker

What's the bijection between reals and infinite sequences of integers?