Inspired by Leibniz's dictum on the identity of indiscernibles, Mycielski introduced the set theoretic axiom LM [JSL, 1995]. In this talk we shall discuss LM and will present the following new results regarding the relationship between LM and other axioms in set theory:
Theorem A. The following are equivalent over ZF:
(1) LM
(2) The global Kinna-Wagner selection principle.
(3) The existence of a definable injection of the universe into the class of subsets of ordinals.
Theorem B. LM is consistent with, and independent of ZFC.

Information:

  Date: Thursday, January 2, 2003, 10:00-12:00
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran

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