""Lambda theory: Introduction of a constant for" nothing" into set theory, a model of consistency and most noticeable conclusions
Logique Et Analyse 222:165-181 (2013)
The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class
|Keywords||nothing void empty set null class Russell Frege Zermelo Lesniewski puzzle model|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Slim Models of Zermelo Set Theory.A. R. D. Mathias - 2001 - Journal of Symbolic Logic 66 (2):487-496.
The Interpretation of Unsolvable $Lambda$-Terms in Models of Untyped $Lambda$-Calculus.Rainer Kerth - 1998 - Journal of Symbolic Logic 63 (4):1529-1548.
Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2013 - Journal of Symbolic Logic 78 (2):543-561.
Rich Models.Michael H. Albert & Rami P. Grossberg - 1990 - Journal of Symbolic Logic 55 (3):1292-1298.
Stationary Sets and Infinitary Logic.Saharon Shelah & Jouko Väänänen - 2000 - Journal of Symbolic Logic 65 (3):1311-1320.
More on Regular Reduced Products.Juliette Cara Kennedy & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (4):1261 - 1266.
A Gitik Iteration with Nearly Easton Factoring.William J. Mitchell - 2003 - Journal of Symbolic Logic 68 (2):481-502.
Topological Representation of the Lambda-Calculus.Steve Awodey - 2000 - Mathematical Structures in Computer Science 10 (1):81-96.
On Regular Reduced Products.Juliette Kennedy & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (3):1169-1177.
Decomposable Ultrafilters and Possible Cofinalities.Paolo Lipparini - 2008 - Notre Dame Journal of Formal Logic 49 (3):307-312.
Recursion Theory and the Lambda-Calculus.Robert E. Byerly - 1982 - Journal of Symbolic Logic 47 (1):67-83.
The Number of Pairwise Non-Elementary-Embeddable Models.Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (4):1431-1455.
The Proofs of $Alpha Rightarrow Alpha$ in $P - W$.Sachio Hirokawa - 1996 - Journal of Symbolic Logic 61 (1):195-211.
Quantification Theory in *8 ofPrincipia Mathematicaand the Empty Domain.Gregory Landini - 2005 - History and Philosophy of Logic 26 (1):47-59.
Added to index2013-12-12
Total downloads98 ( #48,637 of 2,091,802 )
Recent downloads (6 months)16 ( #37,696 of 2,091,802 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.