Switch to: References

Add citations

You must login to add citations.
  1. The 3-Stratifiable Theorems of $\mathit{NFU} \infty$.Marcel Crabbé - 1999 - Notre Dame Journal of Formal Logic 40 (2):174-182.
    It is shown that the 3-stratifiable sentences are equivalent in $\mathit{NFU}$ to truth-functional combinations of sentences about objects, sets of objects, sets of sets of objects, and sentences stating that there are at least $n$ urelements. This is then used to characterize the closed 3-stratifiable theorems of $\mathit{NFU}$ with an externally infinite number of urelements, as those that can be nearly proved in $\mathit{TTU}$ with an externally infinite number of urelements. As a byproduct we obtain a rather simple demonstration of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Systems of combinatory logic related to Quine's ‘New Foundations’.M. Randall Holmes - 1991 - Annals of Pure and Applied Logic 53 (2):103-133.
    Systems TRC and TRCU of illative combinatory logic are introduced and shown to be equivalent in consistency strength and expressive power to Quine's set theory ‘New Foundations’ and the fragment NFU + Infinity of NF described by Jensen, respectively. Jensen demonstrated the consistency of NFU + Infinity relative to ZFC; the question of the consistency of NF remains open. TRC and TRCU are presented here as classical first-order theories, although they can be presented as equational theories; they are not constructive.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Foundations of mathematics in polymorphic type theory.M. Randall Holmes - 2001 - Topoi 20 (1):29-52.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • The 3-Stratifiable Theorems of.Marcel Crabbé - 1999 - Notre Dame Journal of Formal Logic 40 (2):174-182.
    It is shown that the 3-stratifiable sentences are equivalent in to truth-functional combinations of sentences about objects, sets of objects, sets of sets of objects, and sentences stating that there are at least urelements. This is then used to characterize the closed 3-stratifiable theorems of with an externally infinite number of urelements, as those that can be nearly proved in with an externally infinite number of urelements. As a byproduct we obtain a rather simple demonstration of the consistency of 3-stratifiable (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
    		•