Logic List Mailing Archive

Announcement: PoSeT Group Online Seminar on the philosophy of set theory.

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The *PoSeT Group *is glad to announce the second installment of its online
seminar on the philosophy of set theory.

The seminar will be held on *11th November 2024 at 04:30pm CET (UTC +1)*

*Speaker*: *Joan Bagaria (Barcelona)*

*Title*: *On the truth of large cardinal axioms of set theory*

*Abstract*: If we understand set theory as the theory of the set-theoretic
universe, given by the cumulative hierarchy of sets that is obtained
inductively along the class of all ordinal numbers, then all
Zermelo-Fraenkel (ZF) axioms are true. The axiom of Choice is usually taken
also to be true, for a variety of reasons that we?ll not address in this
talk. But as ZFC leaves many fundamental questions about the set-theoretic
universe unanswered, further axioms are needed. Beyond the ZFC axioms, the
axioms asserting the existence of large cardinals are the best studied and
the most widely accepted. But are they true? In recent years, different
forms of varying strength of a very general reflection principle, known as
the principle of Structural Reflection, have been shown equivalent to many
of the known large cardinal axioms, thus providing evidence that all large
cardinal axioms are in essence strong reflection principles of this sort.
We shall discuss to what extent these Structural Reflection principles can
be justified as being true axioms of set theory.

Find out more on the website page: https://www.posetg.org/seminars

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Best,

PoSeT - Group
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