I was puzzeling with the almost standard definition of completeness: In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula ...
The study of Gentzen's sequent calculus give me the opportunity to propose some reflections about the concept of logical truth. I'll refer to the english edition of Gentzen's works : The collected ...
I have some doubts about the "natural" interpretation of $\bot$ in Natural Deduction and sequent calculus. In Prawitz (1965) $\bot$ (falsehood or absurdity) is called a sentential constant [page 14] ...
In logic, it is said that each sentence in a (consistent) theory is either true or false in a given model. Checking the truth of a sentence in a finite model amounts essentially to finite enumeration ...
I graduated in Computer Science at University of Bologna in Italy some years ago. For various reasons now I am discovering a back interest in mathematic logic higher than I was a student. I have only ...
I was wondering if it is possible to define exactly what a non-constructive (nc) proof is. I have often seen the concept associated with the use of principles such as the axiom of choice or the law of ...
If there are two different proofs for one theorem, at some level are the two proofs the same, or can they be fundamentally different? In other words, if you have two proofs of a theorem, can one show ...
The motivation for this question is : http://math.stackexchange.com/questions/4066/rationals-of-the-form-fracpq-where-p-q-are-primes-in-a-b and some other problems in Mathematics which looks as if ...
An extreme form of constructivism is called finitisim. In this form, unlike the standard axiom system, infinite sets are not allowed. There are important mathematicians, such as Kronecker, who ...