Undecidability in Diagonalizable Algebras
Shavrukov, V. Yu.
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 79-116 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
If a formal theory $T$ is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator $\square$ which sends a sentence $\varphi$ to the sentence $\square\varphi$ asserting the provability of $\varphi$ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.
Publié le : 1997-03-14
Classification:  
@article{1183745186,
     author = {Shavrukov, V. Yu.},
     title = {Undecidability in Diagonalizable Algebras},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 79-116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745186}
}

Shavrukov, V. Yu. Undecidability in Diagonalizable Algebras. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  79-116. http://gdmltest.u-ga.fr/item/1183745186/