morphisms-of-computational-structures
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prathyvsh
Non-Wellfoundedness and Foundations
A curation on some reads in the direction of non-wellfoundedness with emphasis on their significance for mathematical foundations.
1/ Sets as Graphs
Alexander Ioan Tomescu (2011) https://www.cs.helsinki.fi/u/tomescu/PhDThesis-AT.pdf A thesis addressing how to see sets as graphs.
2/ Digraphs in terms of set theory
? https://math.unm.edu/~loring/links/graph_s05/basics.pdf
A short paper showing how to visualize sets as directed graphs
3/ Non-wellfounded sets in HoTT
Håkon Robbestad Gylterud June 21, 2020 https://hott-uf.github.io/2020/HoTTUF_2020_paper_19.pdf
Work addressing the significance of non-wellfounded sets in homotopy type theory
4/ Hypersolver: A Graphical Tool for Commonsense Set Theory
Müjdat Pakkan, Varol Akman (1995) https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.4540&rep=rep1&type=pdf
A neat looking tool for representing hypersets and sets
5/ Predicativity, Circularity, and Anti-Foundation
M. Rathjen (2008) https://www1.maths.leeds.ac.uk/~rathjen/russelle.pdf
An attempt to develop the anti-foundational axiom from a predicative vantage point
6/ Mapping sets and hypersets into numbers
Giovanna D’Agostino, Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu (2015)
https://air.uniud.it/retrieve/handle/11390/1069229/40032/DOPT.pdf
A paper showing how sets and hypersets can give a representation for numbers
7/ Non-Wellfounded Set Theory and the Circular Semantics of Semantic Networks
Robin K. Hill (1995)
Applies non-wellfounded set theory for semantic knowledge representation
8/ On non-wellfounded multisets: Scott Collapse in the Multiworld
Giovanna D’Agostino, Albert Visser https://festschriften.illc.uva.nl/j50/contribs/dagostinovisser/dagostinovisser.pdf
Uses Scott bisimulation to define and describe the theory of non-wellfounded multisets
9/ A Cook’s Tour of Non-Well-Founded Sets
Samson Abramsky
A look at finitary non-wellfounded sets from different vantage points: process models, metric approximation, topology and the Vietoris construction, modal logic and Stone duality, and domain theory.
http://www.cs.ox.ac.uk/samson.abramsky/dg05.pdf
10/ Concepts of Set (Slides)
Luca Incurvati https://staff.fnwi.uva.nl/u.endriss/teaching/lolaco/2014/slides/Incurvati.pdf
Set of slides on the conception of set from Luca Incurvati. Also the author of Graph conceptions of set.
