A formal language is a set of strings over an alphabet, defined by precise rules. It's crucial in computer science…
The Turing thesis, also known as the Church-Turing thesis, posits that any function computable by an algorithm can be computed…
A function computable by a Turing machine, representing the theoretical limit of what can be calculated. It forms the basis…
A total function is a mathematical function that is defined for every possible input in its domain. This guarantees an…
The successor function, denoted S(n) = n + 1, is a foundational concept in arithmetic and logic, defining the next…
Strong completeness in logic means that if a formula is true in all interpretations (semantically valid), it can be proven…
A semi-decidable theory allows for an algorithm to list all its theorems. However, it may not offer a way to…
A relative consistency proof demonstrates that if a system S is consistent, adding new axioms to S also maintains consistency.…
A theory with a recursive set of axioms that can derive all its theorems through logical deduction. This property is…
A provability predicate, often denoted as 'Bew', is a fundamental concept in formal logic. It allows us to express within…