Dear enthusiastic logicians and partisans of Logic:
On Wednesday August 5th our recent PhD Alfredo Roque Freite will
give a talk focusing on some results of his PhD Thesis on foundations
of set theory.
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Colloquium Logicae @CLE-Unicamp
This is a virtual session of the Colloquium Logicae,traditional
conferences held at the Centre for Logic, Epistemology and the History
of Science at Unicamp,now linked to the “Logic Supergroup”.
August 5th, 2020 (2:00 PM, GMT -3 hours) –
Alfredo Roque Freire
Post-Doc Researcher
Centre for Logic, Epistemology and the History of Science
University of Campinas-Unicamp, Brazil
"Unreducible features of set theories"
The universalist position in set theory maintains that there is only a
single, maximal universe of sets and, as a result, all sentences about
these objects are ideally verifiable. Often, those who subscribe to
this view are committed to offering a sensible account to alternative
universes familiar to many mathematicians. In this article, we will
analyze the reduction strategies offered by universalists. Recently,
Enayat in [1] proved that no two models of ZF are bi-interpretable,
while Hamkins and I in [2] proved that no two well-founded models of
ZF are mutually interpretable. In view of these results, we will argue
that the range of the construction for alternative universes in a
single universe is limited. Thus, the adherents of an alternative
universe have sufficient grounds to reject the alleged copy offered by
the universalist as a faithful copy. Finally, we will argue that the
reasons for adding new elements to the multiverse should be specific
instead of being the result of an emulation in a previously known
universe.
[1] Enayat, A. (2017). Variations on a Visserian theme. arXiv preprint
arXiv:1702.07093.
[2] Freire, A. R., & Hamkins, J. D. (2020). Bi-interpretation in weak
set theories. arXiv preprint arXiv:2001.05262.