16 papers
A Reunion of Godel, Tarski, Carnap, and Rosser
Saeed Salehi
We unify Godel's First Incompleteness Theorem (1931), Tarski's Undefinability Theorem (1933), Godel-Carnap's Diagonal Lemma (1934), and Rosser's (strengthening of Godel's first) In…
On Godel's "Much Weaker" Assumption
Saeed Salehi
Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if th…
Tarski's Undefinability Theorem and Diagonal Lemma
Saeed Salehi
We prove the equivalence of the semantic version of Tarski's theorem on the undefinability of truth with a semantic version of the Diagonal Lemma, and also show the equivalence of…
On the Truth of Gödelian and Rosserian Sentences
Ziba Assadi, Saeed Salehi
There is a longstanding debate in the logico-philosophical community as to why the Gödelian sentences of a consistent and sufficiently strong theory are true. The prevalent argumen…
From Intuitionism to Many-Valued Logics through Kripke Models
Saeed Salehi
Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Kurt Gödel (1932), and it is proved by Stanisław Jaśkowski (1936) to be a countably many value…
Axiomatic (and Non-Axiomatic) Mathematics
Saeed Salehi
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; b…