PL EN


Journal
2010 | 18 | 3(71) | 79-103
Article title

A NEW POSTULATE OF SET THEORY - THE LEIBNIZ-MYCIELSKI AXIOM (Nowy postulat teorii mnogosci - aksjomat Leibniza-Mycielskiego)

Authors
Title variants
Languages of publication
PL
Abstracts
EN
In this article the authors presents 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 indiscernibles. These models are called Leibnizian models of set theory. The author shows that this additional axiom is equivalent to some choice principles within the axiomatic set theory. It is also indicated that this axiom is derivable from the axiom which states that all sets are ordinal definable (V=OD) within ZF. Finally, the author explains why the process of language skolemization implies the existence of indiscernibles. In his considerations the author follows the ontological and epistemological paradigm of investigations
Journal
Year
Volume
18
Issue
Pages
79-103
Physical description
Document type
ARTICLE
Contributors
  • Piotr Wilczek, Politechnika Poznanska, Instytut Matematyki, ul. Piotrowo 3a, 60-965 Poznan, Poland.
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
10PLAAAA088812
YADDA identifier
bwmeta1.element.5fbc767a-2ad0-3099-b91a-900b29313fcb
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