models of arithmetic
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2021 ◽  
Vol 18 (5) ◽  
pp. 473-502
Author(s):  
Andrew Tedder

The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics. Furthermore, there are general methods for constructing inconsistent models of arithmetic from consistent models, and the theories of such inconsistent models seem likely to differ in terms of complexity. In this paper, I begin to explore this terrain, working, particularly, in incon- sistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals.


Author(s):  
Cezary Cieśliński

AbstractWe present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.


2021 ◽  
Author(s):  
Ali Enayat ◽  
Joel David Hamkins ◽  
Bartosz Wcisło

2019 ◽  
Vol 65 (2) ◽  
pp. 212-217
Author(s):  
Athar Abdul‐Quader ◽  
Roman Kossak
Keyword(s):  

2018 ◽  
Vol 169 (6) ◽  
pp. 487-513 ◽  
Author(s):  
Saeideh Bahrami ◽  
Ali Enayat

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