A remark on equivalent Rosser sentences

@article{Blow2008ARO,
  title={A remark on equivalent Rosser sentences},
  author={Christopher von B{\"u}low},
  journal={Ann. Pure Appl. Log.},
  year={2008},
  volume={151},
  pages={62-67}
}

Rosser-Type Undecidable Sentences Based on Yablo’s Paradox

It is proved that the undecidability of each instance of Rosser-type formalizations of Yablo’s paradox for each consistent but not Σ1-sound theory is dependent on the choice of a standard proof predicate.

SELF-REFERENCE IN ARITHMETIC I

How the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed points for the formULae are obtained is described.

A NOTE ON DERIVABILITY CONDITIONS

It is shown that Hilbert–Bernays’ conditions and Löb’s conditions are mutually incomparable, and it is demonstrated that neither Hilbert– Bernays' conditions nor Lölb's conditions accomplish Gödel's original statement of the second incompleteness theorem.

SELF-REFERENCE IN ARITHMETIC II

In this sequel to Self-reference in arithmetic I, it is investigated how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed point for the expressing formULae are obtained.

GÖDEL’S SECOND INCOMPLETENESS THEOREM: HOW IT IS DERIVED AND WHAT IT DELIVERS

  • S. Salehi
  • Mathematics
    The Bulletin of Symbolic Logic
  • 2020
Abstract The proofs of Gödel (1931), Rosser (1936), Kleene (first 1936 and second 1950), Chaitin (1970), and Boolos (1989) for the first incompleteness theorem are compared with each other,

References

SHOWING 1-7 OF 7 REFERENCES

The logic of provability

1. GL and other systems of propositional modal logic 2. Peano arithmetic 3. The box as Bew(x) 4. Semantics for GL and other modal logics 5. Completeness and decidability of GL and K, K4, T, B, S4,

Models of Peano arithmetic

  • R. Kaye
  • Mathematics
    Oxford logic guides
  • 1991
This chapter discusses the development of the standard model for Peano arithmetic, which combines discretely ordered rings with a collection of prime models to achieve saturation.

Rosser sentences

  • Annals of Mathematical Logic 16 (1)
  • 1979

Annals of mathematical logic

Self-Reference and Modal Logic

0. Introduction.- 1. The Incompleteness Theorems.- 2. Self-Reference.- 3. Things to Come.- 4. The Theory PRA.- 5. Encoding Syntax in PRA.- 6. Additional Arithmetic Prerequisites.- I. The Logic of

Mathematical Logic, Addison-Wesley Series in Logic

  • Mathematical Logic, Addison-Wesley Series in Logic
  • 1967