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Addition and multiplication of sets
 Mathematical Logic Quarterly
, 2007
"... Key words Ordinal arithmetic, adduction, finite set theory. ..."
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Cited by 7 (0 self)
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Key words Ordinal arithmetic, adduction, finite set theory.
Reflections on Skolem's Paradox
"... In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's theorem and the Lö ..."
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Cited by 4 (2 self)
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In 1922, Thoraf Skolem published a paper titled "Some remarks on Axiomatized Set Theory". The paper presents a new proof of... This dissertation focuses almost exclusively on the first half of this project  i.e., the half which tries to expose an initial tension between Cantor's theorem and the LöwenheimSkolem theorem. I argue that, even on quite naive understandings of set theory and model theory, there is no such tension. Hence, Skolem's Paradox is not a genuine paradox, and there is very little reason to worry about (or even to investigate) the more extreme consequences that are supposed to follow from this paradox. The heart of my...
Finite Sets and Counting
, 809
"... These notes present an approach to obtaining the basic properties of the natural numbers in terms of the properties of finite sets (which are introduced independently of the natural numbers). The role played by the usual recursion theorem is taken over by a construction which ..."
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These notes present an approach to obtaining the basic properties of the natural numbers in terms of the properties of finite sets (which are introduced independently of the natural numbers). The role played by the usual recursion theorem is taken over by a construction which