tõestatavus

Tõestatavus refers to the property of a statement, claim, or proposition to be capable of being proven true. In mathematics and logic, this involves demonstrating that a conclusion necessarily follows from a set of axioms or premises through a valid chain of reasoning. A statement is considered provable if a formal proof exists, where each step is justified by established rules or previously proven theorems.

The concept of provability is central to formal systems. Within a given axiomatic system, a statement is either provable or not provable. The set of all provable statements forms the theory of that system. Gödel's incompleteness theorems famously showed that for any sufficiently powerful formal system, there will always be statements that are true but not provable within that system.

In computer science, tõestatavus is crucial in areas like program verification, where the goal is to prove that a program behaves according to its specifications. This often involves using formal methods and logical reasoning to demonstrate the correctness of algorithms and software. The strength of a proof determines the level of confidence in the tõestatavus of a statement.