The Bernays-Schönfinkel-Ramsey class for set theory: decidability

2012 ◽  
Vol 77 (3) ◽  
pp. 896-918 ◽  
Author(s):  
Alberto Policriti ◽  
Eugenio Omodeo
Keyword(s):  
Set Theory ◽  
Decidability Result

AbstractAs proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.

The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability

2010 ◽  
Vol 75 (2) ◽  
pp. 459-480 ◽  
Author(s):  
Eugenio Omodeo ◽  
Alberto Policriti
Keyword(s):  
Set Theory ◽  
Analogous Result ◽  
Forthcoming Paper ◽  
Order Logic ◽  
First Order Logic ◽  
Semantic Approach ◽  
Decidability Result ◽  
First Order ◽  
Generic Set ◽  
Well Foundedness

AbstractAs is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀*-sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper.

A Course on Set Theory

2009 ◽  
Author(s):  
Ernest Schimmerling
Keyword(s):  
Set Theory

Set Theory

2016 ◽  
Author(s):  
Daniel W. Cunningham
Keyword(s):  
Set Theory
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