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- Parvin Safari, Saeed Salehi
- Soft Comput.
- 2018

Kripke frames (and models) provide a suitable semantics for ub-classical logics; for example Intuitionistic Logic (of Brouwer and He yting) axiomatizes the reflexive and transitive Kripke framesâ€¦ (More)

- Saeed Salehi
- Fundam. Inform.
- 2018

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 (solely) theâ€¦ (More)

- Saeed Salehi, Payam Seraji
- Ann. Pure Appl. Logic
- 2018

The proofs of Chaitin and Boolos for GÃ¶delâ€™s Incompleteness Theorem are studied from the perspectives of constructibility and Rosserizability. By Rosserization of a proof we mean that theâ€¦ (More)

- Saeed Salehi
- ArXiv
- 2017

The multiplicative theory of a set of numbers is the theory of the structure of that set with (solely) the multiplication operation (that set is taken to be multiplicative, i.e., closed underâ€¦ (More)

- Saeed Salehi, Payam Seraji
- J. Log. Comput.
- 2017

GÃ¶delâ€™s First Incompleteness Theorem is generalized to definable theories, which are not necessarily recursively enumerable, by using a syntactic-semantic notion (that is the consistency of a theoryâ€¦ (More)

- Ziba Assadi, Saeed Salehi
- ArXiv
- 2017

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 finitelyâ€¦ (More)

- Saeed Salehi
- 2016

Paradoxes are amazing puzzles in philosophy (and mathematics), and they can be interesting when turned into proofs and theorems (in mathematics and logic). For example, Russell's paradox, whichâ€¦ (More)

- Saeed Salehi
- ArXiv
- 2016

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 domains. By GÃ¶delâ€™sâ€¦ (More)

- Saeed Salehi
- ArXiv
- 2016

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 some remain open.â€¦ (More)

- Saeed Salehi
- ArXiv
- 2015

We present a version of GÃ¶delâ€™s Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of theâ€¦ (More)