How does Löb’s theorem, formulated by mathematical logician Martin Hugo Löb, relate to Gödel’s?
The sentence that Gödel constructed is one which asserts its own non-provability, and that sentence must be true but not provable (in the axiom system under consideration). The logician Leon Henkin then constructed a sentence which asserted that it WAS provable, and this sentence is either both true and provable or neither true nor provable, but is it provable or not? This remained an unsolved problem for many years until it was finally solved affirmatively (the sentence IS provable) by a theorem of Martin Löb, which also generalized Gödel’s great Second Incompleteness Theorem, which is that for each of the systems under consideration, the system cannot prove its own consistency! Löb’s theorem also opened up a whole new field of modal logic known as the logic of provability. Q: What are you currently working on in the world of logic? A: These days I work on topics connected with self-reference, which of course ties in with Gödel’s work and with computer science, as well as on my combin
