bio  website  jdh.hamkins.org 

location  New York City  
age  
visits  member for  5 years, 2 months 
seen  6 mins ago  
stats  profile views  50,380 
I am a professor at the City University of New York, at the College of Staten Island and the CUNY Graduate Center, living in midtown Manhattan. My main research interest lies in mathematical logic, particularly set theory, focusing on the mathematics and philosophy of the infinite. A principal concern has been the interaction of forcing and large cardinals, two central concepts in set theory. I have worked in group theory and its interaction with set theory in the automorphism tower problem, and in computability theory, particularly the infinitary theory of infinite time Turing machines. Recently, I am preoccupied with the settheoretic multiverse, engaging with the emerging field known as the philosophy of set theory.
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Questions about ordering of reals and irrationals
Yes; so just use your favorite representation (say, the one without tailing $1$s), and there is no problem. 
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Isomorphic subcategories of directed graphs and presets
Could you tell me what it means to be full? 
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Are hyperreal numbers isomorphic to formal power series?
Todd, one may refer to $\sin(\omega)$ or $e^\omega$ for any hyperreal $\omega$, including infinite elements, simply by appealing to the transfer principleevery function on the reals has a nonstandard analogue, which satisfies all the same firstorder expressible properties in the hyperreals that the original function did in the standard reals. 
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Are hyperreal numbers isomorphic to formal power series?
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answered  Are hyperreal numbers isomorphic to formal power series? 
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Image of poset with Hausdorff interval topology
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Image of poset with Hausdorff interval topology
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answered  Image of poset with Hausdorff interval topology 
Jan 22 
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Is there a compendium of the consistency strength between the most important formal theories?
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Jan 22 
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Is there a compendium of the consistency strength between the most important formal theories?
Can anyone explain to me how to make the images a little smaller? 
Jan 22 
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Is there a compendium of the consistency strength between the most important formal theories?
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Jan 22 
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Is there a compendium of the consistency strength between the most important formal theories?
@EmilJeřábek I suppose the phrase, "strong theories like ZFC" is a matter of perspective! In the large cardinal hierarchy, where of course consistency strength issues loom large, one views ZFC as a weak theory. :) 
Jan 22 
answered  Is there a compendium of the consistency strength between the most important formal theories? 
Jan 21 
awarded  Notable Question 
Jan 19 
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A categorical method to, say, determine the cardinality of a group
For example, can you identify all and only the groups $G$ with cardinality exactly $\aleph_{\omega^2+6}$ by some purely categorytheoretic feature? I expect that at least one such group is identifiable this way, and so if we had the equinumerosity relation, we'll have identified them all. 
Jan 19 
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A categorical method to, say, determine the cardinality of a group
That is, we want to show $G\leq H$ if and only if $\varphi(G,H)$ holds in the category of groups, where $\varphi$ is some purely categorytheoretic statement to be interpreted in that category in a suitable formal language (or prove that there is no such statement). 
Jan 19 
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A categorical method to, say, determine the cardinality of a group
I'm not really satisfied with the $\text{Hom}(\mathbb{Z},G)$ manner of answering this question, since evaluating the cardinality of a Hom set seems to me to be a settheoretic activity rather than a categorical one. A more satisfying answer would be to show that the relation $G\leq H$ for groups $G$ and $H$ is definable (or not) purely in the category of groups, in some formal language appropriate for that category, one able to mention certain kinds of diagrams and whatnot. The "straightedge and compass" that needs to be defined is what precisely this formal language is. 
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A “mother of all groups”? What kind of structures have “mother of all”s?
How could I argue with that? 