McCabe, Gordon (2010) The nonunique Universe. [Preprint]
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Abstract
The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Godel's incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of nonisomorphic but elementarily equivalent models, and classes of model which are both nonisomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model.
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Item Type:  Preprint  

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Keywords:  Multiverses; Godel's incompleteness theorem; theories of everything; mathematical logic; model theory  
Subjects:  Specific Sciences > Physics > Cosmology Specific Sciences > Mathematics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory 

Depositing User:  Gordon McCabe  
Date Deposited:  23 Jan 2010  
Last Modified:  07 Oct 2010 15:19  
Item ID:  5132  
URI:  http://philsciarchive.pitt.edu/id/eprint/5132 
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The nonunique Universe. (deposited 02 Jul 2009)
 The nonunique Universe. (deposited 23 Jan 2010) [Currently Displayed]
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