# The model theory of set-theoretic mereology, Notre Dame Math Logic Seminar, February 2022

This will be a talk for the Mathematical Logic Seminar at the University of Notre Dame on 8 February 2022 at 2 pm in 125 Hayes Healy.

Abstract. Mereology, the study of the relation of part to whole, is often contrasted with set theory and its membership relation, the relation of element to set. Whereas set theory has found comparative success in the foundation of mathematics, since the time of Cantor, Zermelo and Hilbert, mereology is strangely absent. Can a set-theoretic mereology, based upon the set-theoretic inclusion relation ⊆ rather than the element-of relation ∈, serve as a foundation of mathematics? How well is a model of set theory ⟨M,∈⟩ captured by its mereological reduct ⟨M,⊆⟩? In short, how much set theory does set-theoretic mereology know? In this talk, I shall present results on the model theory of set-theoretic mereology that lead broadly to negative answers to these questions and explain why mereology has not been successful as a foundation of mathematics. (Joint work with Makoto Kikuchi)

See the research papers:

• Set-theoretic mereology
• J. D. Hamkins and M. Kikuchi, “Set-theoretic mereology,” Logic and Logical Philosophy, Special issue “Mereology and beyond, part II”, vol. 25, iss. 3, p. 285–308, 2016.
[Bibtex]
@ARTICLE{HamkinsKikuchi2016:Set-theoreticMereology,
author = {Joel David Hamkins and Makoto Kikuchi},
title = {Set-theoretic mereology},
journal = {Logic and Logical Philosophy, Special issue Mereology and beyond, part II''},
editor = {A.~C.~Varzi and R.~Gruszczy{\'n}ski},
year = {2016},
volume = {25},
number = {3},
pages = {285--308},
month = {},
doi = {10.12775/LLP.2016.007},
note = {},
eprint = {1601.06593},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/set-theoretic-mereology},
abstract = {},
keywords = {},
source = {},
ISSN = {1425-3305},
MRCLASS = {03A05 (03E70)},
MRNUMBER = {3546211},
}
• The inclusion relations of the countable models of set theory are all isomorphic
• J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic,” ArXiv e-prints, 2017.
[Bibtex]
@ARTICLE{HamkinsKikuchi:The-inclusion-relations-of-the-countable-models-of-set-theory-are-all-isomorphic,
author = {Joel David Hamkins and Makoto Kikuchi},
title = {The inclusion relations of the countable models of set theory are all isomorphic},
journal = {ArXiv e-prints},
editor = {},
year = {2017},
volume = {},
number = {},
pages = {},
month = {},
doi = {},
note = {Manuscript under review},
eprint = {1704.04480},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/inclusion-relations-are-all-isomorphic},
abstract = {},
keywords = {under-review},
source = {},
}

## 2 thoughts on “The model theory of set-theoretic mereology, Notre Dame Math Logic Seminar, February 2022”

• Looks great, Zach, I’ll be sure to mention your results!