September 2005 The axiom of elementary sets on the edge of Peircean expressibility
Andrea Formisano, Eugenio G. Omodeo, Alberto Policriti
J. Symbolic Logic 70(3): 953-968 (September 2005). DOI: 10.2178/jsl/1122038922


Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987.

The main achievement of this paper is the proof that the ‘kernel’ set theory whose postulates are extensionality, (E), and single-element adjunction and removal, (W) and (L), cannot be axiomatized by means of three-variable sentences. This highlights a sharp edge to be crossed in order to attain an ‘algebraization’ of Set Theory. Indeed, one easily shows that the theory which results from the said kernel by addition of the null set axiom, (N), is in its entirety expressible in three variables.


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Andrea Formisano. Eugenio G. Omodeo. Alberto Policriti. "The axiom of elementary sets on the edge of Peircean expressibility." J. Symbolic Logic 70 (3) 953 - 968, September 2005.


Published: September 2005
First available in Project Euclid: 22 July 2005

zbMATH: 1100.03042
MathSciNet: MR2155274
Digital Object Identifier: 10.2178/jsl/1122038922

Keywords: n-variable expressibility , pebble games , Weak set theories

Rights: Copyright © 2005 Association for Symbolic Logic


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Vol.70 • No. 3 • September 2005
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