This is a try to summarize the most important results of Goedels theorems.

• A statement is provable within a theory if and only if it is true for any interpretation allowed in this theory.

• If a statement is true for some interpretation (model) and false for some other, then it is independent of the theory and undecidable within the theory.

• But the fact, that a statement is undecidable within a theory, cannot be proven within the theory itself. A stronger theory might prove this undecidability, or might not.

• Any theory, that is strong enough, that the representation theorem holds for it, is incomplete, that means, that there are true statements, not provable within it.

• Finally, a theory cannot prove its own consistency.

This is a try to summarize the most important results of Gödel's theorems.

• A statement is provable within a theory if and only if it is true for any interpretation allowed in this theory.

• If a statement is true for some interpretation (model) and false for some other, then it is independent of the theory and undecidable within the theory.

• But the fact, that a statement is undecidable within a theory, cannot be proven within the theory itself. A stronger theory might prove this undecidability, or might not.

• Any theory, that is strong enough, that the representation theorem holds for it, is incomplete, that means, that there are true statements, not provable within it.

• Finally, a theory cannot prove its own consistency.