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Tuesday, 31 March 2026 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Ansten Mørch Klev, Institute of Philosophy of the Czech Academy of Sciences<br />
Title: Inductively defined domains
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Abstract <br />
<p>An intuitive description of the cumulative hierarchy might run as follows: whenever you have certain sets, ā, you may form the set of them, {ā}. Such a description of how the elements of a domain D are built up from below is called a fundamental inductive definition, and the domain D is called inductively defined. The given description of the cumulative hierarchy is, however, not a rigorous definition, since we have not made precise what it means to "have certain sets, ā". I will present Per Martin-Löf's constructive type theory as a theory of inductively defined domains. The cumulative hierarchy will be seen to be only one of infinitely many examples. Based on Martin-Löf's semantical explanations of his type theory, I will also try to explain how an element of an inductively defined domain may be regarded as a well-founded, in general infinite, labelled tree.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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