10 citations · 52 across the 24 of their papers we have counts for
24 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…
Sometime a Paradox, Now Proof: Non-First-Order-izability of Yablo's Paradox
Saeed Salehi
Paradoxes are interesting puzzles in philosophy and mathematics, and they could be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be t…
On the Notions of Rudimentarity, Primitive Recursivity and Representability of Functions and Relations
Saeed Salehi
It is quite well-known from Kurt Godel's (1931) ground-breaking result on the Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are prim…
First-Order Continuous Induction, and a Logical Study of Real Closed Fields
Saeed Salehi, Mohammadsaleh Zarza
Over the last century, the principle of "induction on the continuum" has been studied by different authors in different formats. All of these different readings are equivalent to o…
On Decidability of the Ordered Structures of Numbers
Ziba Assadi, Saeed Salehi
The ordered structures of natural, integer, rational and real numbers are studied here. It is known that the theories of these numbers in the language of order are decidable and fi…
On Axiomatizability of the Multiplicative Theory of Numbers
Saeed Salehi
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (sole…
Computation in Logic and Logic in Computation
Saeed Salehi
The theory of addition in the domains of natural (N), integer (Z), rational (Q), real (R) and complex (C) numbers is decidable, so is the theory of multiplication in all those doma…
Axiomatizing Mathematical Theories: Multiplication
Saeed Salehi
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and…
On Constructivity and the Rosser Property: a closer look at some Gödelean proofs
Saeed Salehi, Payam Seraji
The proofs of Kleene, Chaitin and Boolos for Gödel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incomp…
Kripke Semantics for Fuzzy Logics
Parvin Safari, Saeed Salehi
Kripke frames (and models) provide a suitable semantics for sub-classical logics, for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive…
On Arithmetical Truth of the Self-Referential Sentences
Kaave Lajevardi, Saeed Salehi
We take an argument of Gödel's from his ground-breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: the sentence says about itself th…
Theorems of Tarski's Undefinability and Godel's Second Incompleteness-Computationally
Saeed Salehi
We present a version of Gödel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic v…
Godel-Rosser's Incompleteness Theorems for Non-Recursively Enumerable Theories
Saeed Salehi, Payam Seraji
Godel's First Incompleteness Theorem is generalized to definable theories, which are not necessarily recursively enumerable, by using a couple of syntactic-semantic notions, one is…
Theoremizing Yablo's Paradox
Ahmad Karimi, Saeed Salehi
To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in…
Diagonalizing by Fixed-Points
Ahmad Karimi, Saeed Salehi
A universal schema for diagonalization was popularized by N. S. Yanofsky (2003) in which the existence of a (diagonolized-out and contradictory) object implies the existence of a f…
Godel's Incompleteness Phenomenon - Computationally
Saeed Salehi
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion…
Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories
Saeed Salehi
We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of whose Herbrand Consistenc…
Separating Bounded Arithmetics by Herbrand Consistency
Saeed Salehi
The problem of separating the hierarchy of bounded arithmetic has been studied in the paper. It is shown that the notion of Herbrand Consistency, in its full generality, cann…
Herbrand Consistency of Some Arithmetical Theories
Saeed Salehi
Gödel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the wit…