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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
Recursively Saturated Nonstandard Models of Arithmetic
Wilkie considered models expandable to "strong theories" and complemented Friedman's embeddability criteria with elementary embeddable and isomorphism criteria and invoked this expandability property in order to complement Friedman.
Elementary extensions of recursively saturated models of arithmetic
A countable recursively saturated model of arithmetic has, up to isomorphism, a unique countable recursively saturated elementary end extension. As one might guess from the countability restriction,
On Axiomatizing Fragments
  • C. Smorynski
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1 December 1977
Fixed point algebras
Algebra rarely has anything deep to say about logic. Most applications of algebra to logic are fairly shallow, the exceptions being applications of representation theory, where one is really using