A New Postulate of Set Theory – The Leibniz-Mycielski Axiom

• Authors: Piotr Wilczek

Title variants

PL

Nowy postulat teorii mnogości – aksjomat Leibniza-Mycielskiego

EN

A New Postulate of Set Theory – The Leibniz-Mycielski Axiom

• Languages of publication: PL

Abstracts

PL

In this article we will present the Leibniz-Mycielski axiom (LM) of set theory (ZF) introduced several years ago by Jan Mycielski as an additional axiom of set theory. This new postulate formalizes the so-called Leibniz Law (LL) which states that there are no two distinct indiscernible objects. From the Ehrenfeucht-Mostowski theorem it follows that every theory which has an infinite model has a model with indiscernibles. The new LM axiom states that there are infinite models without indis-cernibles. These models are called Leibnizian models of set theory. We will show that this additional axiom is equivalent to some choice principles within the axio-matic set theory. We will also indicate that this axiom is derivable from the axiom which states that all sets are ordinal definable (V=OD) within ZF. Finally, we will explain why the process of language skolemization implies the existence of indis-cernibles. In our considerations we will follow the ontological and epistemological paradigm of investigations.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 2010
• Volume: 18
• Issue: 3
• Pages: 79-103

Dates

published

2010-09-01

Contributors

author

Piotr Wilczek